Existence, nonexistence and multiplicity results for nonlocal Dirichlet problems

DOI10.1016/j.jde.2018.10.046zbMath1420.35095OpenAlexW2899616764MaRDI QIDQ1736191

Alexander Quaas, Gonzalo Dávila, Erwin Topp

Publication date: 26 March 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.10.046

zbMATH Keywords

eigenvaluesfully nonlinear Dirichlet problemHamilton-Jocobi equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items

Periodic solutions for one-dimensional nonlinear nonlocal problem with drift including singular nonlinearities ⋮ Ambrosetti-Prodi type results for Dirichlet problems of fractional Laplacian-like operators ⋮ Viscosity Solutions for Nonlocal Equations with Space-Dependent Operators ⋮ The nonlocal inverse problem of Donsker and Varadhan ⋮ Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term ⋮ Existence and multiplicity results for a critical superlinear fractional Ambrosetti-Prodi type problem ⋮ Hopf's lemma for viscosity solutions to a class of non-local equations with applications ⋮ Interior regularity results for fractional elliptic equations that degenerate with the gradient ⋮ Cauchy problem and periodic homogenization for nonlocal Hamilton–Jacobi equations with coercive gradient terms ⋮ Harnack inequality and self-similar solutions for fully nonlinear fractional parabolic equations ⋮ Risk-sensitive control for a class of diffusions with jumps

Cites Work

• Unnamed Item
• Boundary regularity for fully nonlinear integro-differential equations
• Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations
• Nonuniqueness of solutions for Dirichlet problems related to fully nonlinear singular or degenerate operators
• On the strong maximum principle for second order nonlinear parabolic integro-differential equations
• Regularity for solutions of nonlocal, nonsymmetric equations
• A note on a nonlinear Krein-Rutman theorem
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators
• Controlled Markov processes and viscosity solutions
• Regularity theory for fully nonlinear integro-differential equations
• Exit Time Problems in Optimal Control and Vanishing Viscosity Method
• User’s guide to viscosity solutions of second order partial differential equations
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Nonuniqueness for the Dirichlet Problem for Fully Nonlinear Elliptic Operators and the Ambrosetti–Prodi Phenomenon
• Resonance Phenomena for Second-Order Stochastic Control Equations
• On the Dirichlet problem for second-order elliptic integro-differential equations
• Holder estimates for solutions of integro differential equations like the fractional laplace
• Applied stochastic control of jump diffusions