Two-phase problems with distributed sources: regularity of the free boundary

By D. Silva, Fausto Ferrari, Sandro Salsa. 2012

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We investigate the regularity of the free boundary for a general class of two-phase free boundary problems with non-zero right hand side. We prove that Lipschitz or flat free boundaries are $C^{1,\gamma}$. In particular, viscosity solutions are indeed classical.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8318cba6fa93107f4e4953cc8d8130736ff62889