Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
This work examines \(\lambda\)-caloric functions which are nonnegative solutions of the heat equation \(\Delta u- \lambda u_t= 0\) \((\lambda> 0)\) in some domain that vanishes locally on some distinguished part of the boundary. Caloric functions in Lipschitz domains are shown to be monotone in any direction going into the domain. Regularity of solutions of certain free boundary problems across the transition surface is developed, which involves the study of asymptotic behavior of caloric functions on the boundary.
scientific article; zbMATH DE number 906871