A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition

DOI10.1007/S00526-015-0912-4zbMath1334.35439OpenAlexW1468104775MaRDI QIDQ5963581

Luis A. Caffarelli, Pei-Yong Wang

Publication date: 22 February 2016

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-015-0912-4

zbMATH Keywords

uniquenessphase transitionbifurcation phenomenonmountain pass lemmaone-phase free boundary problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Initial-boundary value problems for second-order parabolic equations (35K20) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35) Weak solutions to PDEs (35D30) Bifurcations in context of PDEs (35B32) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

The one-phase bifurcation for the \(p\)-Laplacian ⋮ A bifurcation phenomenon in a singularly perturbed two-phase free boundary problem of phase transition ⋮ Symmetry and approximate symmetry of a nonlinear elliptic problem over a ring

Cites Work

• On the uniqueness of a solution of a two-phase free boundary problem
• Uniform Lipschitz regularity of a singular perturbation problem
• User’s guide to viscosity solutions of second order partial differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition