Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1161 - 1199

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian...

60G12 | 60G22 | Secondary 60G20 | Gaussian spatiotemporal white noise measure | Riemannan-Liouville fractional integral and derivative | Dirichlet regular bounded open domains | stochastic boundary value problems | eigenfunction expansion | Mittag-Leffler function | Primary 60G60 | 60G17 | Caputo-Djrbashian fractional-in-time derivative | fractional pseudodifferential elliptic operators | 60G15 | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | NOISE | DRIVEN | DIFFUSION EQUATION | RANDOM-FIELDS | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | RANDOM-WALK | WAVE-EQUATIONS | Random noise theory | Stochastic differential equations | Research | Mathematical research

60G12 | 60G22 | Secondary 60G20 | Gaussian spatiotemporal white noise measure | Riemannan-Liouville fractional integral and derivative | Dirichlet regular bounded open domains | stochastic boundary value problems | eigenfunction expansion | Mittag-Leffler function | Primary 60G60 | 60G17 | Caputo-Djrbashian fractional-in-time derivative | fractional pseudodifferential elliptic operators | 60G15 | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | NOISE | DRIVEN | DIFFUSION EQUATION | RANDOM-FIELDS | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | RANDOM-WALK | WAVE-EQUATIONS | Random noise theory | Stochastic differential equations | Research | Mathematical research

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 01/2016, Volume 19, Issue 5, pp. 1161 - 1199

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian...

Functions (mathematics) | Asymptotic properties | Mathematical analysis | Eigenvalues | Dirichlet problem | Evolution | Calculus | Polynomials

Functions (mathematics) | Asymptotic properties | Mathematical analysis | Eigenvalues | Dirichlet problem | Evolution | Calculus | Polynomials

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 02/2019, Volume 179, pp. 309 - 343

In this paper, we establish boundary partial regularity for weak solutions to the equations of stationary motion of electrorheological fluids with homogeneous...

Electrorheological fluid | Partial regularity | Weak solution | Regularity up to the boundary | Variable exponent | EXISTENCE | MATHEMATICS, APPLIED | NONLINEAR ELLIPTIC-SYSTEMS | MOTIONS | MINIMIZERS | INTEGRALS | MATHEMATICS | WEAK SOLUTIONS | Variables | Domains | Partial differential equations | Electrorheological fluids | Boundary conditions | Dirichlet problem | Regularity

Electrorheological fluid | Partial regularity | Weak solution | Regularity up to the boundary | Variable exponent | EXISTENCE | MATHEMATICS, APPLIED | NONLINEAR ELLIPTIC-SYSTEMS | MOTIONS | MINIMIZERS | INTEGRALS | MATHEMATICS | WEAK SOLUTIONS | Variables | Domains | Partial differential equations | Electrorheological fluids | Boundary conditions | Dirichlet problem | Regularity

Journal Article

Potential Analysis, ISSN 0926-2601, 2/2015, Volume 42, Issue 2, pp. 335 - 363

In this note we study the Dirichlet problem associated with a version of prime end boundary of a bounded domain in a complete metric measure space equipped...

31B25 | Perron method | p -harmonic functions | Probability Theory and Stochastic Processes | Mathematics | 30L99 | 31C15 | Metric measure spaces | Primary: 31E05 | Poincaré inequality | Secondary: 31B15 | Geometry | Prime end boundary | Potential Theory | Functional Analysis | Dirichlet problem | Doubling measure | p-harmonic functions | MATHEMATICS | SOBOLEV FUNCTIONS | Poincare inequality | EXTENSION

31B25 | Perron method | p -harmonic functions | Probability Theory and Stochastic Processes | Mathematics | 30L99 | 31C15 | Metric measure spaces | Primary: 31E05 | Poincaré inequality | Secondary: 31B15 | Geometry | Prime end boundary | Potential Theory | Functional Analysis | Dirichlet problem | Doubling measure | p-harmonic functions | MATHEMATICS | SOBOLEV FUNCTIONS | Poincare inequality | EXTENSION

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 08/2015, Volume 40, Issue 8, pp. 1467 - 1497

Given a selfadjoint, elliptic operator L, one would like to know how the spectrum changes as the spatial domain Ω ⊂ ℝ n is deformed. For a family of domains {Ω...

35B05 | Secondary: 53D12 | Primary: 35P15 | Morse index | 35J25 | Domain deformation | Elliptic boundary value problem | Maslov index | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRAL FLOW | Partial differential equations | Operators | Theorems | Spectral theory | Dirichlet problem | Boundary conditions | Boundaries | Subspaces

35B05 | Secondary: 53D12 | Primary: 35P15 | Morse index | 35J25 | Domain deformation | Elliptic boundary value problem | Maslov index | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRAL FLOW | Partial differential equations | Operators | Theorems | Spectral theory | Dirichlet problem | Boundary conditions | Boundaries | Subspaces

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 11/2019, Volume 234, Issue 2, pp. 453 - 507

In a bounded domain $${\mathcal {O}}\subset {\mathbb {R}}^3$$ O ⊂ R 3 of class $$C^{1,1}$$ C 1 , 1 , we consider a stationary Maxwell system with the perfect...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | DIRICHLET PROBLEM | MATHEMATICS, APPLIED | MECHANICS | ELLIPTIC-SYSTEMS | ERROR ESTIMATE | OPERATOR | Magnetic fields | Permeability | Electric properties | Magnetic induction | Divergence | Mathematical analysis | Magnetic permeability | Boundary conditions | Maxwell's equations | Matrix methods

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | DIRICHLET PROBLEM | MATHEMATICS, APPLIED | MECHANICS | ELLIPTIC-SYSTEMS | ERROR ESTIMATE | OPERATOR | Magnetic fields | Permeability | Electric properties | Magnetic induction | Divergence | Mathematical analysis | Magnetic permeability | Boundary conditions | Maxwell's equations | Matrix methods

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 7/2005, Volume 91, Issue 1, pp. 249 - 272

Given an open set Ω of compact closure in Rm, the classical Dirichlet problem is to extend a given continuous function ψ : ∂ Ω → R to a continuous function...

Alexandrov curvature | Dirichlet problem | harmonic map | geodesic space | Riemannian manifold | Riemannian polyhedron | UPPER BOUNDED CURVATURE | MATHEMATICS | MAPPINGS | METRIC-SPACES | RIEMANNIAN POLYHEDRA

Alexandrov curvature | Dirichlet problem | harmonic map | geodesic space | Riemannian manifold | Riemannian polyhedron | UPPER BOUNDED CURVATURE | MATHEMATICS | MAPPINGS | METRIC-SPACES | RIEMANNIAN POLYHEDRA

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 8/2010, Volume 297, Issue 3, pp. 653 - 686

We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain $${\Omega\subset\mathbb{R}^2}$$ , which is not necessarily simply...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | ENERGY | UP SOLUTIONS | CONCENTRATING SOLUTIONS | LARGE EXPONENT | 2-DIMENSIONAL ELLIPTIC PROBLEM | DIRICHLET PROBLEM | PHYSICS, MATHEMATICAL | QUALITATIVE PROPERTIES

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | ENERGY | UP SOLUTIONS | CONCENTRATING SOLUTIONS | LARGE EXPONENT | 2-DIMENSIONAL ELLIPTIC PROBLEM | DIRICHLET PROBLEM | PHYSICS, MATHEMATICAL | QUALITATIVE PROPERTIES

Journal Article

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 10/2017, Volume 147, Issue 5, pp. 895 - 916

In this note semi-bounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and...

Dirichlet-Neumann map | Boundary triple | Weyl function | Elliptic differential operator | Semi-bounded operator | SPECTRAL THEORY | EIGENVALUE | MATHEMATICS, APPLIED | ELLIPTIC DIFFERENTIAL-OPERATORS | LAPLACIAN | MATHEMATICS | boundary triple | RESOLVENT FORMULAS | LARGE PARAMETER | DOMAINS | semi-bounded operator | elliptic differential operator | Operators (mathematics) | Partial differential equations | Differential equations | Dirichlet–Neumann map | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Dirichlet-Neumann map | Boundary triple | Weyl function | Elliptic differential operator | Semi-bounded operator | SPECTRAL THEORY | EIGENVALUE | MATHEMATICS, APPLIED | ELLIPTIC DIFFERENTIAL-OPERATORS | LAPLACIAN | MATHEMATICS | boundary triple | RESOLVENT FORMULAS | LARGE PARAMETER | DOMAINS | semi-bounded operator | elliptic differential operator | Operators (mathematics) | Partial differential equations | Differential equations | Dirichlet–Neumann map | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2014, Volume 266, Issue 7, pp. 4314 - 4421

We prove that given any , for each open set and any closed subset of such that is locally an -domain near , there exists a linear and bounded extension...

Bessel potential space and capacity | Synthesis | Locally [formula omitted]-domain | Mixed boundary value problem | Higher-order elliptic system | Ahlfors regular set | Linear extension operator | Besov and Triebel–Lizorkin spaces | Higher-order Sobolev space | Higher-order boundary trace operator | Real and complex interpolation | Locally (ε, δ)-domain | Besov and Triebel-Lizorkin spaces | DIFFERENTIABLE FUNCTIONS | Locally (epsilon, delta)-domain | STOKES SYSTEM | BESOV-SPACES | LIPSCHITZ-DOMAINS | EXTENSION-THEOREMS | INTERPOLATION | MATHEMATICS | DECOMPOSITIONS | REGULARITY | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS

Bessel potential space and capacity | Synthesis | Locally [formula omitted]-domain | Mixed boundary value problem | Higher-order elliptic system | Ahlfors regular set | Linear extension operator | Besov and Triebel–Lizorkin spaces | Higher-order Sobolev space | Higher-order boundary trace operator | Real and complex interpolation | Locally (ε, δ)-domain | Besov and Triebel-Lizorkin spaces | DIFFERENTIABLE FUNCTIONS | Locally (epsilon, delta)-domain | STOKES SYSTEM | BESOV-SPACES | LIPSCHITZ-DOMAINS | EXTENSION-THEOREMS | INTERPOLATION | MATHEMATICS | DECOMPOSITIONS | REGULARITY | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2019, Volume 277, Issue 5, pp. 1499 - 1530

We consider the Dirichlet problem and the weak Dirichlet problem on a general, possibly nonregular bounded domain, for elliptic linear equation with uniformly...

Dirichlet problem | Elliptic equation | Martin boundary | Trace operator | MATHEMATICS | PRINCIPLE | ABSOLUTE CONTINUITY | Computer science

Dirichlet problem | Elliptic equation | Martin boundary | Trace operator | MATHEMATICS | PRINCIPLE | ABSOLUTE CONTINUITY | Computer science

Journal Article

12.
Full Text
Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular spaces

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2019, Volume 474, Issue 2, pp. 852 - 875

We use sphericalization to study the Dirichlet problem, Perron solutions and boundary regularity for -harmonic functions on unbounded sets in Ahlfors regular...

Ahlfors regular metric space | Boundary regularity | Perron solutions of the Dirichlet problem | Sphericalization | Muckenhoupt [formula omitted] weight | p-harmonic functions and measures | weight | Muckenhoupt A | MATHEMATICS, APPLIED | QUASIMINIMIZERS | POTENTIAL-THEORY | BOUNDARY-REGULARITY | PRESERVATION | MATHEMATICS | RESPECT | Muckenhoupt A(p) weight | MAZURKIEWICZ BOUNDARY | SETS | DIRICHLET PROBLEM | PERRON METHOD | KELLOGG PROPERTY | Naturvetenskap | Matematisk analys | Ahlfors regular metric space; Boundary regularity; Muckenhoupt A(p) weight; Perron solutions of the Dirichlet problem; p-harmonic functions and measures; Sphericalization | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Ahlfors regular metric space | Boundary regularity | Perron solutions of the Dirichlet problem | Sphericalization | Muckenhoupt [formula omitted] weight | p-harmonic functions and measures | weight | Muckenhoupt A | MATHEMATICS, APPLIED | QUASIMINIMIZERS | POTENTIAL-THEORY | BOUNDARY-REGULARITY | PRESERVATION | MATHEMATICS | RESPECT | Muckenhoupt A(p) weight | MAZURKIEWICZ BOUNDARY | SETS | DIRICHLET PROBLEM | PERRON METHOD | KELLOGG PROPERTY | Naturvetenskap | Matematisk analys | Ahlfors regular metric space; Boundary regularity; Muckenhoupt A(p) weight; Perron solutions of the Dirichlet problem; p-harmonic functions and measures; Sphericalization | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Journal Article

Mathematika, ISSN 0025-5793, 1/2006, Volume 58, Issue 2, pp. 1 - 25

We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain Ω in ℝN. We consider deformations ϕ(Ω) of Ω...

35J25 | 47A75 | 47B25 (primary) | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | EIGENFUNCTIONS | DIRICHLET

35J25 | 47A75 | 47B25 (primary) | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | EIGENFUNCTIONS | DIRICHLET

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 3/2012, Volume 72, Issue 3, pp. 345 - 361

We study the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value...

Primary 45P05 | Analysis | layer potential | fractional Laplacian | Boundary integral operator | Mathematics | Secondary 30E25 | bounded Lipschitz domain | SYSTEM | MATHEMATICS | FRACTALS | CYLINDERS | HEAT-EQUATION | DIRICHLET PROBLEM | LAYER POTENTIALS

Primary 45P05 | Analysis | layer potential | fractional Laplacian | Boundary integral operator | Mathematics | Secondary 30E25 | bounded Lipschitz domain | SYSTEM | MATHEMATICS | FRACTALS | CYLINDERS | HEAT-EQUATION | DIRICHLET PROBLEM | LAYER POTENTIALS

Journal Article

15.
Full Text
Estimates of Solutions and Asymptotic Symmetry for Parabolic Equations on Bounded Domains

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2007, Volume 183, Issue 1, pp. 59 - 91

We consider fully nonlinear parabolic equations on bounded domains under Dirichlet boundary conditions. Assuming that the equation and the domain satisfy...

Mechanics | Fluids | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | Complexity | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | CONVERGENCE | MONOTONICITY | SYSTEMS | Studies | Dirichlet problem | Estimates

Mechanics | Fluids | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | Complexity | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | CONVERGENCE | MONOTONICITY | SYSTEMS | Studies | Dirichlet problem | Estimates

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 12/2018, Volume 291, Issue 17-18, pp. 2516 - 2535

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov...

fractional Cauchy problem | infinitesimal generator | 26A33 | 35S11 | bounded domain | killed Feller process | 60J35 | 60K99 | APPROXIMATION | DISPERSION | EQUATIONS | DRIVEN | CAUCHY | MATHEMATICS | NUMERICAL-SOLUTION | RANDOM-WALKS | LEVY MOTION | DIFFUSION | Markov processes

fractional Cauchy problem | infinitesimal generator | 26A33 | 35S11 | bounded domain | killed Feller process | 60J35 | 60K99 | APPROXIMATION | DISPERSION | EQUATIONS | DRIVEN | CAUCHY | MATHEMATICS | NUMERICAL-SOLUTION | RANDOM-WALKS | LEVY MOTION | DIFFUSION | Markov processes

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 8/2014, Volume 54, Issue 8, pp. 1261 - 1279

The Dirichlet problem is considered on the junction of thin quantum waveguides (of thickness h ≪ 1) in the shape of an infinite two-dimensional ladder. Passage...

Computational Mathematics and Numerical Analysis | quantum graph | lattice of quantum waveguides | Kirchhoff transmission conditions | cross-shaped waveguide | Dirichlet spectral problem | Mathematics | Dirichlet condition | bounded solutions at threshold | MATHEMATICS, APPLIED | PERTURBATIONS | PHYSICS, MATHEMATICAL | TRAPPED MODES | EIGENVALUES | ASYMPTOTICS | DOMAINS | Waveguides | Studies | Dirichlet problem | Mathematical analysis | Quantum physics | Asymptotic properties | Graphs | Mathematical models | Spectra | Two dimensional | Ladders

Computational Mathematics and Numerical Analysis | quantum graph | lattice of quantum waveguides | Kirchhoff transmission conditions | cross-shaped waveguide | Dirichlet spectral problem | Mathematics | Dirichlet condition | bounded solutions at threshold | MATHEMATICS, APPLIED | PERTURBATIONS | PHYSICS, MATHEMATICAL | TRAPPED MODES | EIGENVALUES | ASYMPTOTICS | DOMAINS | Waveguides | Studies | Dirichlet problem | Mathematical analysis | Quantum physics | Asymptotic properties | Graphs | Mathematical models | Spectra | Two dimensional | Ladders

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 06/2015, Volume 119, pp. 254 - 274

In this paper, we study the existence of a positive local in time solution for the following singular nonlinear problem with homogeneous Dirichlet boundary...

[formula omitted]-Laplace equation | Log-Sobolev inequalities | Singular parabolic equation | p-Laplace equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | POSITIVE SOLUTIONS | STABILIZATION | DEGENERATE | SYSTEMS | ELLIPTIC-EQUATIONS | Infinity | Mathematical analysis | Triangles | Inequalities | Dirichlet problem | Texts | Nonlinearity | Constants

[formula omitted]-Laplace equation | Log-Sobolev inequalities | Singular parabolic equation | p-Laplace equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | POSITIVE SOLUTIONS | STABILIZATION | DEGENERATE | SYSTEMS | ELLIPTIC-EQUATIONS | Infinity | Mathematical analysis | Triangles | Inequalities | Dirichlet problem | Texts | Nonlinearity | Constants

Journal Article

Annals of PDE, ISSN 2199-2576, 12/2016, Volume 2, Issue 2, pp. 1 - 42

We consider the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove global a priori...

Mathematical Methods in Physics | Global regularity | Nonlinear maximum principle | Bounded domains | 35Q35 | SQG | 35Q86 | Physics | Partial Differential Equations

Mathematical Methods in Physics | Global regularity | Nonlinear maximum principle | Bounded domains | 35Q35 | SQG | 35Q86 | Physics | Partial Differential Equations

Journal Article

Mathematische Annalen, ISSN 0025-5831, 09/2006, Volume 336, Issue 1, pp. 73 - 110

Let D be a homogeneous Siegel domain of type II. We prove that every bounded Hua-harmonic function F on D is pluriharmonic. The proof is based on asymptotic...

58J32 | Mathematics, general | Mathematics | 14M17 | 32M10 | 35J25 | 34E05 | SYSTEM | MATHEMATICS | SPACES | IRREDUCIBLE SIEGEL DOMAINS | DIRICHLET PROBLEM | NORM | EIGENFUNCTIONS | OPERATORS | BERGMAN LAPLACIAN

58J32 | Mathematics, general | Mathematics | 14M17 | 32M10 | 35J25 | 34E05 | SYSTEM | MATHEMATICS | SPACES | IRREDUCIBLE SIEGEL DOMAINS | DIRICHLET PROBLEM | NORM | EIGENFUNCTIONS | OPERATORS | BERGMAN LAPLACIAN

Journal Article