Symmetry Results for Fractional Elliptic Systems and Related Problems
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Publication:5256316
DOI10.1080/03605302.2014.1003073zbMath1322.35163arXiv1402.1193OpenAlexW2950189877MaRDI QIDQ5256316
Publication date: 22 June 2015
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1402.1193
Fractional partial differential equations (35R11) Entire solutions to PDEs (35B08) Symmetries, invariants, etc. in context of PDEs (35B06) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)
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Cites Work
- Unnamed Item
- De Giorgi type results for elliptic systems
- A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian
- On De Giorgi's conjecture in dimension \(N\geq 9\)
- Regularity of the extremal solutions associated to elliptic systems
- Stable solutions of \(-\Delta u = f(u)\) in \(\mathbb R^N\)
- Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
- Asymptotic behavior of solutions of elliptic equations. I: Liouville-type theorems for linear and nonlinear equations on \(R^ n\).
- Asymptotic behavior of solutions of elliptic equations. II: Analogues of Liouville's theorem for solutions of inequalities on \(R^ n\), \(n\geq 3\)
- On a conjecture of De Giorgi and some related problems
- New Liouville theorems for linear second order degenerate elliptic equations in divergence form.
- Regularity of flat level sets in phase transitions
- Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
- Hamiltonian identities for elliptic partial differential equations
- Sharp energy estimates for nonlinear fractional diffusion equations
- A Liouville theorem for non local elliptic equations
- Regularity theory for fully nonlinear integro-differential equations
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- On the structure of phase transition maps for three or more coexisting phases
- An Extension Problem Related to the Fractional Laplacian
- Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
- On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property
