A convergence of the approximated free boundary of regularized functionals via \(\varGamma \)-convergence

DOI10.1016/J.CAM.2007.07.010zbMath1225.65066OpenAlexW1996592472MaRDI QIDQ932735

Yoshihiko Yamaura

Publication date: 11 July 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.07.010

zbMATH Keywords

variational problemfree boundaryRadon measuresnon-degeneracy\(\varGamma \)-convergence

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Methods involving semicontinuity and convergence; relaxation (49J45) Free boundary problems for PDEs (35R35) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Cites Work

• A gradient flow of the one-dimensional Alt-Caffarelli functional
• \(\Gamma\)-convergence and numerical analysis: An application to the minimal partition problem
• A free boundary problem for a quasilinear elliptic equation. I: Rectifiability of free boundary
• An introduction to \(\Gamma\)-convergence
• A construction of a Lipschitz continuous minimizer of a free boundary problem
• A singular limit arising in combustion theory: Fine properties of the free boundary
• The gradient theory of phase transitions and the minimal interface criterion
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Uniform estimates and limits for a two phase parabolic singular perturbation problem
• A Free-Boundary Problem for the Heat Equation Arising in Flame Propagation
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