Saddle-shaped solutions for the fractional Allen-Cahn equation
From MaRDI portal
Publication:1677406
DOI10.3934/dcdss.2018024zbMath1375.35195OpenAlexW2765690292MaRDI QIDQ1677406
Publication date: 21 November 2017
Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdss.2018024
Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11) Entire solutions to PDEs (35B08)
Related Items (3)
Semilinear integro-differential equations. II: One-dimensional and saddle-shaped solutions to the Allen-Cahn equation ⋮ Uniqueness and stability of the saddle-shaped solution to the fractional Allen-Cahn equation ⋮ Semilinear integro-differential equations. I. Odd solutions with respect to the Simons cone
Cites Work
- Nonlocal diffusion and applications
- Regularity of nonlocal minimal cones in dimension 2
- \(\Gamma \)-convergence for nonlocal phase transitions
- On De Giorgi's conjecture in dimension \(N\geq 9\)
- Uniqueness and stability of saddle-shaped solutions to the Allen-Cahn equation
- Some constructions for the fractional Laplacian on noncompact manifolds
- Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
- Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
- Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
- Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
- Saddle solutions of the bistable diffusion equation
- On a conjecture of De Giorgi and some related problems
- Rigidity of minimizers in nonlocal phase transitions
- Global minimizers of the Allen-Cahn equation in dimension \(n\geq 8\)
- A three-dimensional symmetry result for a phase transition equation in the genuinely nonlocal regime
- Nonlocal \(s\)-minimal surfaces and Lawson cones
- Positive solutions for non local elliptic problems
- Quantitative flatness results and \(BV\)-estimates for stable nonlocal minimal surfaces
- Regularity of flat level sets in phase transitions
- Regularity and Bernstein-type results for nonlocal minimal surfaces
- Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
- Minimal cones and the Bernstein problem
- Sharp energy estimates for nonlinear fractional diffusion equations
- Solutions of the fractional Allen–Cahn equation which are invariant under screw motion
- Saddle-shaped solutions of bistable elliptic equations involving the half-Laplacian
- A concave—convex elliptic problem involving the fractional Laplacian
- Qualitative Properties of Saddle-Shaped Solutions to Bistable Diffusion Equations
- Improvement of Flatness for Nonlocal Phase Transitions
- Nonlocal minimal surfaces
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- On the stability of the saddle solution of Allen–Cahn's equation
- An Extension Problem Related to the Fractional Laplacian
- Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
- Layer solutions in a half‐space for boundary reactions
- On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property
This page was built for publication: Saddle-shaped solutions for the fractional Allen-Cahn equation
