Some Remarks on the Duality Method for Integro-Differential Equations with Measure Data
From MaRDI portal
Publication:2789501
DOI10.1515/ans-2015-5014zbMath1382.35331arXiv1409.8463OpenAlexW3099531758MaRDI QIDQ2789501
Publication date: 1 March 2016
Published in: Advanced Nonlinear Studies (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.8463
Smoothness and regularity of solutions to PDEs (35B65) Integro-partial differential equations (45K05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs with measure (35R06)
Related Items
The Dirichlet problem for the \(p\)-fractional Laplace equation ⋮ On singular equations involving fractional Laplacian ⋮ Singular nonlocal problem involving measure data ⋮ A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions ⋮ New characterizations of Morrey spaces and their preduals with applications to fractional Laplace equations ⋮ Renormalized and entropy solutions for the fractional \(p\)-Laplacian evolution equations ⋮ On uniqueness and structure of renormalized solutions to integro-differential equations with general measure data ⋮ On semilinear elliptic equations with diffuse measures ⋮ Nonlocal semilinear elliptic problems with singular nonlinearity ⋮ A fractional Laplacian problem with mixed singular nonlinearities and nonregular data ⋮ Existence of a unique positive entropy solution to a singular fractional Laplacian ⋮ On positive viscosity solutions of fractional Lane-Emden systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
- Boundary regularity for fully nonlinear integro-differential equations
- Hitchhiker's guide to the fractional Sobolev spaces
- A duality approach to the fractional Laplacian with measure data
- On \(L_p\)-estimates for a class of non-local elliptic equations
- Regularity results for nonlocal equations by approximation
- Regularity results for stable-like operators
- A priori estimates for integro-differential operators with measurable kernels
- Estimates on Green functions and Poisson kernels for symmetric stable processes
- Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels: subcritical case
- On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik boundary point principle
- The Dirichlet problem for nonlocal operators
- Some remarks about the summability of nonlocal nonlinear problems
- Nonlocal equations with measure data
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Weak and viscosity solutions of the fractional Laplace equation
- Semilinear fractional elliptic equations involving measures
- The extremal solution for the fractional Laplacian
- Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
- Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures
- From the long jump random walk to the fractional Laplacian
- Nonlinear Diffusion with Fractional Laplacian Operators
- Non-local Dirichlet forms and symmetric jump processes
- Regularity theory for fully nonlinear integro-differential equations
- Weakly Differentiable Functions
- Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
- On the Dirichlet problem for second-order elliptic integro-differential equations
