Some perspectives on (non)local phase transitions and minimal surfaces

DOI10.1142/s1664360723300013zbMath1520.53006arXiv2207.04783OpenAlexW4321790891MaRDI QIDQ6040538

Publication date: 17 May 2023

Published in: Bulletin of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.04783

zbMATH Keywords

phase transition minimal surfaces regularity theory

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Phase transitions (general) in equilibrium statistical mechanics (82B26) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11)

Cites Work

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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 $\mathbb{R}^3$
Local and global minimizers for a variational energy involving a fractional norm
Regularity of nonlocal minimal cones in dimension 2
Density estimates for a variational model driven by the Gagliardo norm
Some monotonicity results for minimizers in the calculus of variations
The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
$\Gamma $-convergence for nonlocal phase transitions
Boundary behavior of nonlocal minimal surfaces
Extensions of Moser-Bangert theory. Locally minimal solutions
On De Giorgi's conjecture in dimension $N\geq 9$
On the oriented Plateau problem
Stable $s$-minimal cones in $\mathbb{R}^3$ are flat for $s \sim 1$
Boundary properties of fractional objects: flexibility of linear equations and rigidity of minimal graphs
Some connections between results and problems of De Giorgi, Moser and Bangert
Slope-changing solutions of elliptic problems on $\mathbb R^n$
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
$\Gamma$ convergence of an energy functional related to the fractional Laplacian
Minimal solutions of variational problems on a torus
On minimal laminations of the torus
On a conjecture of De Giorgi and some related problems
A nonlocal anisotropic model for phase transitions
One-dimensional symmetry of bounded entire solutions of some elliptic equations
Stationary layered solutions in $\mathbb{R}^2$ for a class of non autonomous Allen-Cahn equations
Rigidity of minimizers in nonlocal phase transitions
A three-dimensional symmetry result for a phase transition equation in the genuinely nonlocal regime
Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter
Nonlocal $s$-minimal surfaces and Lawson cones
Symmetry for solutions of semilinear elliptic equations in $\mathbb{R}^N$ and related conjectures
The gradient theory of phase transitions and the minimal interface criterion
Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
Getting acquainted with the fractional Laplacian
Description of an ecological niche for a mixed local/nonlocal dispersal: an evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes
Nonlocal minimal graphs in the plane are generically sticky
On stable solutions for boundary reactions: a De Giorgi-type result in dimension $4 + 1$
Quantitative flatness results and $BV$-estimates for stable nonlocal minimal surfaces
Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media
Regularity of flat level sets in phase transitions
Regularity and Bernstein-type results for nonlocal minimal surfaces
Regularity properties of nonlocal minimal surfaces via limiting arguments
Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
Minimal varieties in Riemannian manifolds
Minimal cones and the Bernstein problem
A gradient estimate for nonlocal minimal graphs
Sharp energy estimates for nonlinear fractional diffusion equations
$1$D symmetry for solutions of semilinear and quasilinear elliptic equations
Planelike minimizers of nonlocal Ginzburg–Landau energies and fractional perimeters in periodic media
1D symmetry for semilinear PDEs from the limit interface of the solution
Long-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn Equation
Flatness results for nonlocal minimal cones and subgraphs
Improvement of Flatness for Nonlocal Phase Transitions
Bernstein and De Giorgi type problems: new results via a geometric approach
Nonlocal minimal surfaces
On a class of minimal cones in $R^n$
Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
Density Estimates for Degenerate Double-Well Potentials
Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness
The Equivariant Plateau Problem and Interior Regularity
Plane-like minimizers in periodic media: jet flows and Ginzburg-Landau-type functionals
Uniform convergence of a singular perturbation problem
A Comparison Between the Nonlocal and the Classical Worlds: Minimal Surfaces, Phase Transitions, and Geometric Flows
Rigidity of Minimizers in Nonlocal Phase Transitions II
Free Energy of a Nonuniform System. I. Interfacial Free Energy
Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
The Physics of Structural Phase Transitions
Layer solutions in a half‐space for boundary reactions
(Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property
On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

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