Long-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn Equation
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Publication:3294736
DOI10.1007/978-3-030-33116-0_5zbMath1442.35128arXiv1803.03850OpenAlexW2792704458MaRDI QIDQ3294736
Enrico Valdinoci, Serena Dipierro
Publication date: 29 June 2020
Published in: CIM Series in Mathematical Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.03850
Related Items (3)
Some perspectives on (non)local phase transitions and minimal surfaces ⋮ Partial differential equations from theory to applications: dedicated to Alberto Farina, on the occasion of his 50th birthday ⋮ Some energy estimates for stable solutions to fractional Allen-Cahn equations
Cites Work
- Unnamed Item
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- Nonlocal diffusion and applications
- Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in \(\mathbb{R}^3\)
- Density estimates for a variational model driven by the Gagliardo norm
- Hitchhiker's guide to the fractional Sobolev spaces
- \(\Gamma \)-convergence for nonlocal phase transitions
- On De Giorgi's conjecture in dimension \(N\geq 9\)
- Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
- Geometry of quasiminimal phase transitions
- 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
- On a conjecture of De Giorgi and some related problems
- A nonlocal anisotropic model for phase transitions
- On De Giorgi's conjecture in dimensions 4 and 5
- One-dimensional symmetry of bounded entire solutions of some elliptic equations
- Rigidity of minimizers in nonlocal phase transitions
- Some remarks on the classification of global solutions with asymptotically flat level sets
- 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
- Symmetry for solutions of semilinear elliptic equations in \(\mathbb{R}^N\) and related conjectures
- Uniqueness and minimality of solutions of a Ginzburg-Landau equation
- Getting acquainted with the fractional Laplacian
- Regularity of flat level sets in phase transitions
- Regularity properties of nonlocal minimal surfaces via limiting arguments
- Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
- Hamiltonian identities for elliptic partial differential equations
- Towards a counter-example to a conjecture of De Giorgi in high dimensions
- Sharp energy estimates for nonlinear fractional diffusion equations
- On the spectrum of two different fractional operators
- Rigidity results for elliptic PDEs with uniform limits: an abstract framework with applications
- $1$D symmetry for solutions of semilinear and quasilinear elliptic equations
- Some results on minimizers and stable solutions of a variational problem
- 1D symmetry for semilinear PDEs from the limit interface of the solution
- Improvement of Flatness for Nonlocal Phase Transitions
- Nonlocal minimal surfaces
- A gradient bound and a liouville theorem for nonlinear poisson equations
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- Uniform convergence of a singular perturbation problem
- Rigidity of Minimizers in Nonlocal Phase Transitions II
- Fractional thoughts
- 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
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