Calculus of Variations and Geometric Measure Theory

G. Palatucci - E. Valdinoci

A weighted gradient theory of phase transitions with a possibly singular and degenerate spatial inhomogeneity

created by palatucci on 17 Feb 2011
modified on 02 Jun 2012


Published Paper

Inserted: 17 feb 2011
Last Updated: 2 jun 2012

Journal: J. Differential Equations
Volume: 252
Pages: 3381-3402
Year: 2012


This paper studies the asymptotic behavior of a perturbed variational prob- lem for the Cahn-Hilliard theory of phase transitions in a fluid, with spatial inhomogeneities in the internal free energy term. The inhomogeneous term can vanish or become infinite and it can also behave as an appropriate power of the distance from the boundary. The standard minimal interface criterion will be recovered even in spite of such severe degeneracies andor singularities.

Keywords: phase transitions, G-convergence, singular perturbation, Spatial inhomogeneity