The role of minimal surfaces in the study of the Allen-Cahn equation

DOI10.1090/conm/570/11306zbMath1273.58011OpenAlexW2954471986MaRDI QIDQ4898199

Frank Pacard

Publication date: 30 December 2012

Published in: Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/570/11306

zbMATH Keywords

minimal surfacesAllen-Cahn equationinfinite dimensional Liapunov-Schimidt reduction

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Minimal surfaces and optimization (49Q05) Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Entire solutions to PDEs (35B08) PDEs on manifolds (35R01) Partial differential equations on manifolds; differential operators (58Jxx)

Related Items (13)

Concentration on curves for a Neumann Ambrosetti-Prodi-type problem in two-dimensional domains ⋮ Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen-Cahn ⋮ The Weyl law for the phase transition spectrum and density of limit interfaces ⋮ Double-well phase transitions are more rigid than minimal hypersurfaces ⋮ On the existence of \(N\)-junctions for a symmetric nonnegative potential with \(N+1\) zeros ⋮ On the triple junction problem without symmetry hypotheses ⋮ Low Complexity Solutions of the Allen–Cahn Equation on Three-spheres ⋮ Concentration on submanifolds for an Ambrosetti-Prodi type problem ⋮ On the Placement of an Obstacle So As to Optimize the Dirichlet Heat Trace ⋮ On the Ambrosetti-Malchiodi-Ni conjecture for general submanifolds ⋮ The second inner variation of energy and the Morse index of limit interfaces ⋮ Gradient estimates for a class of semilinear parabolic equations and their applications ⋮ Variational aspects of phase transitions with prescribed mean curvature

This page was built for publication: The role of minimal surfaces in the study of the Allen-Cahn equation