Large solutions to elliptic equations involving fractional Laplacian
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Publication:896167
DOI10.1016/j.anihpc.2014.08.001zbMath1456.35211arXiv1311.6044OpenAlexW2963832949MaRDI QIDQ896167
Alexander Quaas, Patricio L. Felmer, Huyuan Chen
Publication date: 11 December 2015
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1311.6044
Boundary value problems for second-order elliptic equations (35J25) Semilinear elliptic equations (35J61) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Large \(s\)-harmonic functions and boundary blow-up solutions for the fractional Laplacian
- Local and global minimizers for a variational energy involving a fractional norm
- Fundamental solutions for a class of Isaacs integral operators
- Fundamental solutions and Liouville type theorems for nonlinear integral operators
- The Evans-Krylov theorem for nonlocal fully nonlinear equations
- Regularity results for nonlocal equations by approximation
- On the inequality \(\Delta u \geqq f (u)\)
- Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
- Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs
- `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
- Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
- Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
- Existence and uniqueness results for large solutions of general nonlinear elliptic equations
- Nondegeneracy and uniqueness for boundary blow-up elliptic problems
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Weak and viscosity solutions of the fractional Laplace equation
- Localization on the Boundary of Blow-up for Reaction–Diffusion Equations with Nonlinear Boundary Conditions
- On solutions of δu=f(u)
- Regularity theory for fully nonlinear integro-differential equations
- Fundamental solutions and two properties of elliptic maximal and minimal operators
- Dependence of blowup rate of large solutions of semilinear elliptic equations, on the curvature of the boundary
- Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
- Explosive solutions of quasilinear elliptic equations: existence and uniqueness
- Holder estimates for solutions of integro differential equations like the fractional laplace
- The influence of domain geometry in boundary blow-up elliptic problems.
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