2012, ISBN 9814374342, xi, 241

Book

2012, Graduate studies in mathematics, ISBN 9780821875773, Volume 134, xviii, 414

Book

Calculus of variations and partial differential equations, ISSN 1432-0835, 10/2010, Volume 42, Issue 1-2, pp. 21 - 41

We establish existence and non-existence results to the Brezis–Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero...

35J65 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | Analysis | 35B99 | 35B33 | 35R11 | Mathematics | 58E30 | Physical Sciences | Mathematics, Applied | Science & Technology | Boundary conditions | Dirichlet problem | Partial differential equations | Mathematical analysis | Calculus of variations | Roots

35J65 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | Analysis | 35B99 | 35B33 | 35R11 | Mathematics | 58E30 | Physical Sciences | Mathematics, Applied | Science & Technology | Boundary conditions | Dirichlet problem | Partial differential equations | Mathematical analysis | Calculus of variations | Roots

Journal Article

4.
Full Text
The Laplace Equation

: Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

2018, ISBN 9783319743066, 669

This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains...

Mathematics | Potential Theory | Mathematics and Statistics | Partial Differential Equations | Neumann problem | Dirichlet problem | Poisson equation | Transmission problem | Derivative oblique problem | Robin problem

Mathematics | Potential Theory | Mathematics and Statistics | Partial Differential Equations | Neumann problem | Dirichlet problem | Poisson equation | Transmission problem | Derivative oblique problem | Robin problem

eBook

2015, Other titles in applied mathematics, ISBN 9781611973815, Volume 141, xi, 293

Book

Communications in partial differential equations, ISSN 0360-5302, 11/2017, Volume 42, Issue 11, pp. 1781 - 1836

In this paper, we consider the problem of identifying a connection ∇ on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian...

35R30 (Primary) | Connection Laplacian | Dirichlet-to-Neumann map | inverse problems | X-ray transform | magnetic Schrödinger operator | Calderon problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Bundling | Manifolds | Equivalence | Gaussian beams (optics) | Uniqueness | Geometrical optics | Dirichlet problem | Bundles

35R30 (Primary) | Connection Laplacian | Dirichlet-to-Neumann map | inverse problems | X-ray transform | magnetic Schrödinger operator | Calderon problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Bundling | Manifolds | Equivalence | Gaussian beams (optics) | Uniqueness | Geometrical optics | Dirichlet problem | Bundles

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 03/2014, Volume 101, Issue 3, pp. 275 - 302

We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian...

Fractional Laplacian | Dirichlet problem | Boundary regularity | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Boundary element methods

Fractional Laplacian | Dirichlet problem | Boundary regularity | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Boundary element methods

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 04/2014, Volume 26, Issue 3, p. 1450005

.... The problem can be reformulated in terms of Dirichlet–Neumann operators, and as a side result, we derive a formula for the shape derivative of these operators.

eigenvalue problems | Dirichlet-Neumann operators | perturbation theory | pseudodifferential operators | Physical Sciences | Physics | Physics, Mathematical | Science & Technology

eigenvalue problems | Dirichlet-Neumann operators | perturbation theory | pseudodifferential operators | Physical Sciences | Physics | Physics, Mathematical | Science & Technology

Journal Article

1994, De Gruyter expositions in mathematics, ISBN 9783110135220, Volume 13., vii, 524

Book

Journal of spectral theory, ISSN 1664-039X, 2017, Volume 7, Issue 2, pp. 321 - 359

The Steklov problem is an eigenvalue problem with the spectral parameter in the boundary conditions, which has various applications...

Riemannian manifold | Dirichlet-to-Neumann operator | Steklov eigenvalue problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Riemannian manifold | Dirichlet-to-Neumann operator | Steklov eigenvalue problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Boundary value problems, ISSN 1687-2762, 12/2014, Volume 2014, Issue 1, pp. 1 - 15

We consider a class of particular
(
p
,
2
)
$(p,2)$
-Laplacian Dirichlet problems with a right-hand side nonlinearity which exhibits an asymmetric growth...

Ordinary Differential Equations | Analysis | asymmetric Dirichlet problem | Difference and Functional Equations | Approximations and Expansions | one side resonance | Mathematics, general | Mathematics | Partial Differential Equations | subcritical exponential growth | Physical Sciences | Mathematics, Applied | Science & Technology | Functions, Exponential | Research | Mathematical research | Series, Dirichlet | Laplacian operator | Mountains | Boundary value problems | Theorems | Asymmetry | Mathematical analysis | Inequalities | Dirichlet problem | Texts | Nonlinearity

Ordinary Differential Equations | Analysis | asymmetric Dirichlet problem | Difference and Functional Equations | Approximations and Expansions | one side resonance | Mathematics, general | Mathematics | Partial Differential Equations | subcritical exponential growth | Physical Sciences | Mathematics, Applied | Science & Technology | Functions, Exponential | Research | Mathematical research | Series, Dirichlet | Laplacian operator | Mountains | Boundary value problems | Theorems | Asymmetry | Mathematical analysis | Inequalities | Dirichlet problem | Texts | Nonlinearity

Journal Article

Calculus of variations and partial differential equations, ISSN 0944-2669, 2/2019, Volume 58, Issue 1, pp. 1 - 26

...Calc. Var. (2019) 58:34
https://doi.org/10.1007/s00526-018-1468-x Calculus of Variations
The Helfrich boundary value problem
Sascha Eichmann 1
Received: 13...

35J40 | 58J32 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 49Q10 | 35J35 | 49Q20 | Physical Sciences | Mathematics, Applied | Science & Technology | Mathematics - Analysis of PDEs

35J40 | 58J32 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 49Q10 | 35J35 | 49Q20 | Physical Sciences | Mathematics, Applied | Science & Technology | Mathematics - Analysis of PDEs

Journal Article

Calculus of variations and partial differential equations, ISSN 1432-0835, 12/2017, Volume 57, Issue 1, pp. 1 - 15

We give a necessary and sufficient condition for positive Borel measures such that the Dirichlet problem, with zero boundary data, for the complex Monge...

35J96 | 32U40 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C55 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Computer science

35J96 | 32U40 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C55 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Computer science

Journal Article

Calculus of variations and partial differential equations, ISSN 0944-2669, 2/2018, Volume 57, Issue 1, pp. 1 - 26

We study the following elliptic problem $$-A(u) = \lambda u^q$$
-A(u)=λuq
with Dirichlet boundary conditions, where $$A(u) (x) = \Delta u (x) \chi _{D_1} (x)+ \Delta _p u(x) \chi _{D_2}(x)$$
A(u)(x)=Δu(x)χD1(x)+Δpu(x)χD2(x...

35J20 | 35J62 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J92 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology

35J20 | 35J62 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J92 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

1991, Lecture notes in mathematics, ISBN 3540544860, Volume 1482., vi, 173

Book

Communications in Contemporary Mathematics, ISSN 0219-1997, 02/2017, Volume 19, Issue 1, p. 1550088

In this paper, we study a highly nonlocal parametric problem involving a fractional-type operator combined with a Kirchhoff-type coefficient...

variational methods | Kirchhoff equation | vibrating string | multiple weak solutions | fractional Laplacian | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

variational methods | Kirchhoff equation | vibrating string | multiple weak solutions | fractional Laplacian | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 08/2017, Volume 27, Issue 9, p. 1750136

.... Using hidden symmetry principles, based on an extended problem with periodic boundary conditions and
O
(
2...

equivariant bifurcation | Newton-Krylov continuation | hidden symmetry | Lyapunov-Schmidt reduction | Kuramoto-Sivashinsky equation | Mathematics, Interdisciplinary Applications | Science & Technology - Other Topics | Physical Sciences | Multidisciplinary Sciences | Mathematics | Science & Technology | Mathematics - Dynamical Systems

equivariant bifurcation | Newton-Krylov continuation | hidden symmetry | Lyapunov-Schmidt reduction | Kuramoto-Sivashinsky equation | Mathematics, Interdisciplinary Applications | Science & Technology - Other Topics | Physical Sciences | Multidisciplinary Sciences | Mathematics | Science & Technology | Mathematics - Dynamical Systems

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 07/2017, Volume 17, Issue 3, pp. 429 - 456

This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator...

35J20 | Stationary Kirchhoff–Dirichlet Problems | Critical Nonlinearities | 35J60 | Hardy Coefficients | 35R11 | Variational Methods | 35S15 | Stationary Kirchhoff-Dirichlet Problems | Nonlocal p-Laplacian Operators | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

35J20 | Stationary Kirchhoff–Dirichlet Problems | Critical Nonlinearities | 35J60 | Hardy Coefficients | 35R11 | Variational Methods | 35S15 | Stationary Kirchhoff-Dirichlet Problems | Nonlocal p-Laplacian Operators | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 03/2019, Volume 21, Issue 2, p. 1850019

In this paper, we deal with the composite plate problem, namely the following optimization eigenvalue problem:
inf
ρ
∈
P
inf
u
∈
\
{
0
}
∫
Ω
(
Δ
u
)
2
∫
Ω
ρ...

symmetry of solutions | polarization | biharmonic operator | optimization of eigenvalues | Composite plate problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematics - Analysis of PDEs

symmetry of solutions | polarization | biharmonic operator | optimization of eigenvalues | Composite plate problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematics - Analysis of PDEs

Journal Article