Symmetry of solutions to semilinear equations involving the fractional Laplacian
DOI10.3934/cpaa.2015.14.2393zbMath1328.35289OpenAlexW2525796999MaRDI QIDQ746508
Publication date: 16 October 2015
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/cpaa.2015.14.2393
symmetrymonotonicityDirichlet problemmethod of moving planesfractional Laplaciannonexistence of positive solutionsnarrow region principlesemi-linear elliptic equationdecay at infinitymaximum principle for anti-symmetric functions
Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Liouville theorem for \(\alpha\)-harmonic functions in \(\mathbb{R}^n_+\)
- Liouville type theorems for poly-harmonic Navier problems
- A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
- Radial symmetry and regularity of solutions for poly-harmonic Dirichlet problems
- Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
- Symmetry and monotonicity for a system of integral equations
- Uniqueness of positive solutions of semilinear equations in \(R^ n\).
- Elliptic equations with nearly critical growth
- Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Symmetry and related properties via the maximum principle
- A priori estimates and existence of positive solutions of semilinear elliptic equations
- Regularity of solutions for a system of integral equations
- Inequalities for second-order elliptic equations with applications to unbounded domains. I
- Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system
- Radial symmetry of solutions for some integral systems of Wolff type
- Liouville theorems involving the fractional Laplacian on a half space
- Super poly-harmonic property of solutions for Navier boundary problems on a half space
- Liouville type theorems for Schrödinger system with Navier boundary conditions in a half space
- A Liouville type theorem for an integral system
- Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
- A concave—convex elliptic problem involving the fractional Laplacian
- Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
- Monotonicity and Symmetry of Solutions of Fully Nonlinear Elliptic Equations on Bounded domains
- On the method of moving planes and the sliding method
- An Extension Problem Related to the Fractional Laplacian
- Classification of solutions for an integral equation
- Symmetry via antisymmetric maximum principles in nonlocal problems of variable order
This page was built for publication: Symmetry of solutions to semilinear equations involving the fractional Laplacian
