Abstract
We study a 2-phase free boundary problem, in which the positive and negative parts of a solution satisfy two different elliptic equations, and a condition, involving normal derivatives from positive and negative sides holds on the free boundary in a weak sense. We show that if the free boundary is locally a graph of Lipschitz function, then it is $C^{1,\alpha} $ smooth. This is an extension of the result obtained by L.Caffarelli in the case when the positive and negative parts of a solution satisfy the same elliptic equation.
Citation
Mikhail Feldman. "Regularity for nonisotropic two-phase problems with Lipschitz free boundaries." Differential Integral Equations 10 (6) 1171 - 1179, 1997. https://doi.org/10.57262/die/1367438227
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