Density estimates for phase transitions with a trace

2010/11/30 by Yannick Sire, Enrico Valdinoci, Sire, Yannick +1
Materials Science · Computer Science · Mathematics · #Solidification and crystal growth phenomena #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1011.6617

Abstract

We consider a functional obtained by adding a trace term to the Allen-Cahn phase segregation model and we prove some density estimates for the level sets of the interfaces. We treat in a unified way also the cases of possible degeneracy and singularity of the ellipticity of the model and the quasiminimal case.

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