Regularity of flat level sets in phase transitions. (English) Zbl 1180.35499

The paper deals with Ginzburg-Landau model of phase transitions. Further properties of phase transitions that are similar to the properties of sets with minimal perimeter are established. Some analogies between the theory of phase transitions and the theory of minimal surfaces are explained. The main result of this paper is an “improvement of flatness” theorem for 0 level sets of local minimizers. The method of subsolutions and supersolutions together with the sliding method is used.


35Q56 Ginzburg-Landau equations
35J20 Variational methods for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q05 Minimal surfaces and optimization
Full Text: DOI Link