Mixed local and nonlocal elliptic operators: regularity and maximum principles
From MaRDI portal
Publication:5067724
DOI10.1080/03605302.2021.1998908zbMath1486.35412arXiv2005.06907OpenAlexW3212192528MaRDI QIDQ5067724
Stefano Biagi, Serena Dipierro, Eugenio Vecchi, Enrico Valdinoci
Publication date: 4 April 2022
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.06907
Smoothness and regularity of solutions to PDEs (35B65) Maximum principles in context of PDEs (35B50) Second-order elliptic equations (35J15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions
- Density estimates for a variational model driven by the Gagliardo norm
- Lipschitz regularity of solutions for mixed integro-differential equations
- Hitchhiker's guide to the fractional Sobolev spaces
- Regularity and rigidity theorems for a class of anisotropic nonlocal operators
- Bifurcation results for a fractional elliptic equation with critical exponent in \(\mathbb {R}^n\)
- Viscosity solutions for a system of integro-PDEs and connections to optimal switching and control of jump-diffusion processes
- A Widder's type theorem for the heat equation with nonlocal diffusion
- Convergence of nonlocal threshold dynamics approximations to front propagation
- Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
- On distributional solutions of local and nonlocal problems of porous medium type
- Continuous dependence estimates for viscosity solutions of integro-PDEs
- Pseudo differential operators with negative definite symbols of variable order
- On the strong maximum principle for second order nonlinear parabolic integro-differential equations
- Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications
- Decay estimates for evolutionary equations with fractional time-diffusion
- Getting acquainted with the fractional Laplacian
- Second order linear evolution equations with general dissipation
- Description of an ecological niche for a mixed local/nonlocal dispersal: an evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes
- The Liouville theorem and linear operators satisfying the maximum principle
- Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations
- A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
- Gradient estimates for a class of anisotropic nonlocal operators
- A ``maximum principle for semicontinuous functions applicable to integro-partial differential equations
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Weak and viscosity solutions of the fractional Laplace equation
- Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum
- Boundary Harnack principle for $Δ+ Δ^{𝛼/2}$
- A Priori Bounds for Solutions of a Nonlocal Evolution PDE
- Improvement of Flatness for Nonlocal Phase Transitions
- Harnack inequalities for non-local operators of variable order
- An Elliptic Boundary Value Problem with Fractional Nonlinearity
- Semilinear elliptic equations involving mixed local and nonlocal operators
- Nonexistence Results for Nonlocal Equations with Critical and Supercritical Nonlinearities
- Heat kernel estimates for subordinate Brownian motions
- Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE
- Holder estimates for solutions of integro differential equations like the fractional laplace
- Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order
