In this paper we start to develop the regularity theory of general two-phase free boundary problems for parabolic equations. In particular we consider uniformly parabolic operators in nondivergence form and we are mainly concerned with the optimal regularity of the viscosity solutions. We prove that under suitable nondegenerate conditions the solution is Lipschitz across the free boundary.
F. Ferrari, S. Salsa (2010). Regularity of the Solutions for Parabolic Two-Phase Free Boundary Problems. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 35, 1095-1129 [10.1080/03605301003717126].
Regularity of the Solutions for Parabolic Two-Phase Free Boundary Problems
FERRARI, FAUSTO;
2010
Abstract
In this paper we start to develop the regularity theory of general two-phase free boundary problems for parabolic equations. In particular we consider uniformly parabolic operators in nondivergence form and we are mainly concerned with the optimal regularity of the viscosity solutions. We prove that under suitable nondegenerate conditions the solution is Lipschitz across the free boundary.File in questo prodotto:
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