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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
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
Journal Article
Potential Analysis, ISSN 0926-2601, 2/2015, Volume 42, Issue 2, pp. 335 - 363
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
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 11/2019, Volume 234, Issue 2, pp. 453 - 507
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
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 8/2010, Volume 297, Issue 3, pp. 653 - 686
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
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
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
Journal Article
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
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
Journal Article
Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 8/2014, Volume 54, Issue 8, pp. 1261 - 1279
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
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
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
Journal Article