The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
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Publication:2256555
DOI10.1007/s11118-014-9443-4zbMath1307.31022OpenAlexW2054116999MaRDI QIDQ2256555
Publication date: 19 February 2015
Published in: Potential Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11118-014-9443-4
Robin boundary conditionsfractional Laplacianfractional-order Sobolev spacesNeumann boundary condtions
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Fractional Laplacian: Pohozaev identity and nonexistence results
- Hitchhiker's guide to the fractional Sobolev spaces
- Dirichlet forms and symmetric Markov processes.
- The Pohozaev identity for the fractional Laplacian
- Reflected symmetric \(\alpha\)-stable processes and regional fractional Laplacian
- Integration by parts formula for regional fractional Laplacian
- Variational problems with free boundaries for the fractional Laplacian
- The heat equation with nonlinear generalized Robin boundary conditions
- Quasiconformal mappings and extendability of functions in Sobolev spaces
- The Laplacian with Robin boundary conditions on arbitrary domains
- Censored stable processes
- Dirichlet and Neumann boundary conditions: what is in between?
- Potential theory. An analytic and probabilistic approach to balayage
- On Sobolev and capacitary inequalities for contractive Besov spaces over \(d\)-sets
- On the Dirichlet problem for pseudodifferential operators generating Feller semigroups
- Some quasi-linear elliptic equations with inhomogeneous generalized Robin boundary conditions on ``bad domains
- The \(p\)-Laplace operator with the nonlocal Robin boundary conditions on arbitrary open sets
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
- The extremal solution for the fractional Laplacian
- Boundary value problems for some degenerate-elliptic operators
- Heat kernel estimates for stable-like processes on \(d\)-sets.
- A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions
- Theory of capacities
- Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains
- Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions
- Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises
- A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems
- Dirichlet and Neumann boundary conditions for the p-Laplace operator: what is in between?
- Nonlocal Tug-of-War and the Infinity Fractional Laplacian
- A priori estimates for a class of quasi-linear elliptic equations
- Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
- Robin boundary value problems on arbitrary domains
- Lévy Processes and Stochastic Calculus
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- An Extension Problem Related to the Fractional Laplacian
- Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
- BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS
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