Asymptotic behavior of the interface for entire vector minimizers in phase transitions

DOI10.1016/j.jfa.2022.109565zbMath1497.35025arXiv2112.00796OpenAlexW4281564787MaRDI QIDQ2149497

Nicholas D. Alikakos, Arghir Zarnescu, Zhiyuan Geng

Publication date: 29 June 2022

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.00796

zbMATH Keywords

phase transitionsvector minimizersentire solutionssubquadratic potential

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Entire solutions to PDEs (35B08)

Cites Work

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• Uniform Poincaré-Sobolev and isoperimetric inequalities for classes of domains
• Regularity for degenerate two-phase free boundary problems
• A semilinear PDE with free boundary
• On De Giorgi's conjecture in dimension \(N\geq 9\)
• Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
• The effect of a singular perturbation on nonconvex variational problems
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• On a conjecture of De Giorgi and some related problems
• A minimization problem with free boundary related to a cooperative system
• A homogeneity improvement approach to the obstacle problem
• 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
• Elliptic systems of phase transition type
• Regularity of the free boundary for the vectorial Bernoulli problem
• Equilibrium points of a singular cooperative system with free boundary
• Regularity of flat level sets in phase transitions
• On the existence of connecting orbits for critical values of the energy
• A free boundary problem for an elliptic system
• Symmetric quadruple phase transitions
• Regularity of the free boundary in a two-phase semilinear problem in two dimensions
• A gradient bound and a liouville theorem for nonlinear poisson equations
• The gradient theory of phase transitions for systems with two potential wells
• Local minimisers and singular perturbations
• Partial regularity for weak solutions of an elliptic free boundary problem
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• C^{1, 1} Regularity in semilinear elliptic problems
• Uniform convergence of a singular perturbation problem
• A three-layered minimizer in R2 for a variational problem with a symmetric three-well potential
• On De Giorgi’s conjecture and beyond
• Sliding almost minimal sets and the Plateau problem
• Metric methods for heteroclinic connections
• Phase transitions: Uniform regularity of the intermediate layers
• An obstacle-problem-like equation with two phases: Pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary

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