Variational solutions to nonlocal problems

Variational methods applied to PDEs (35A15) Linear operators on function spaces (general) (47B38) Equations and inequalities involving linear operators, with vector unknowns (47A50) Fractional partial differential equations (35R11) Elliptic operators and their generalizations (47F10)

Cites Work

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Regularity for parabolic integro-differential equations with very irregular kernels
Boundary regularity for fully nonlinear integro-differential equations
Local behavior of fractional \(p\)-minimizers
Nonlocal Harnack inequalities
Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
Mountain pass solutions for non-local elliptic operators
Potential analysis of stable processes and its extensions. With some of the papers based on the presentations at the workshop on stochastic and harmonic analysis of processes with jumps, Angers, France, May 2--9, 2006.
The Dirichlet problem for nonlocal operators with singular kernels: convex and nonconvex domains
A priori estimates for integro-differential operators with measurable kernels
On an open question about functions of bounded variation.
Elliptic partial differential equations of second order
Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
On the Dirichlet problem for pseudodifferential operators generating Feller semigroups
Getting acquainted with the fractional Laplacian
The weak Harnack inequality for the Boltzmann equation without cut-off
Regularity estimates for elliptic nonlocal operators
Function spaces and extension results for nonlocal Dirichlet problems
The Dirichlet problem for nonlocal operators
Boundary regularity estimates for nonlocal elliptic equations in \(C^1\) and \(C^{1,\alpha }\) domains
The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
Local Regularity for Parabolic Nonlocal Operators
Integro-Differential equations with nonlinear directional dependence
Further Time Regularity for Nonlocal, Fully Nonlinear Parabolic Equations
Regularity theory for parabolic nonlinear integral operators
Density Estimates for a Nonlocal Variational Model via the Sobolev Inequality
On the variational limit of a class of nonlocal functionals related to peridynamics
Variational Methods for Nonlocal Fractional Problems
Regularity theory for fully nonlinear integro-differential equations
Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
The boundary Harnack principle for the fractional Laplacian
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
Regularity results for nonlocal parabolic equations
A Brezis-Nirenberg type result for a nonlocal fractional operator
The bond-based peridynamic system with Dirichlet-type volume constraint
Holder estimates for solutions of integro differential equations like the fractional laplace
Monotonicity and nonexistence results for some fractional elliptic problems in the half-space

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