On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations

By Guy Barles, Emmanuel Chasseigne, C. Imbert. 2008

195 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c74fb18cb2896fb4c65d1f0f37c7b818f1165df1

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions (2009, unknown): “1, and the analytic approaches in [3,4].”
Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes (2010, unknown): “for example [1, 2, 6, 7, 17, 29, 30, 31, 38, 39].”
Aleksandrov–Bakelman–Pucci Type Estimates for Integro-Differential Equations (2010, methodology): “Schwab in [2], and the comparison theory for these equations was recently improved and re-presented in [5], with the Dirichlet problem being considered in [3].”
WEAK AND VISCOSITY SOLUTIONS OF THE FRACTIONAL LAPLACE EQUATION (2014, unknown): “Namely, we take ρ ∈ C∞ 0 (B1; [0, 1]) and we consider the mollifier ρε(x) := ε−nρ(x/ε), ε > 0.”
On Neumann Type Problems for nonlocal Equations set in a half Space (2011, background): “We also refer to [4] for results in this direction.”
A Hölder infinity Laplacian (2012, background): “For further reading on viscosity solutions of non-local operators, one can for instance consult [6].”
DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES (2015, background): “Recently, in the literature a deep interest was shown for nonlocal operators, thanks to their intriguing analytical structure and in view of several applications in a wide range of contexts, such as the thin obstacle problem, optimization, finance, phase transitions, stratified materials, anomalous…”
The best constant in a fractional Hardy inequality (2008, background): “We suggest the former as a possible setup for studying Dirichlet boundary value problems for non-local integro-differential operators and the corresponding stochastic processes [30], [38] on subdomains of R [3], beyond the “convolutional” case of the whole of R [4], [21].”