Differential and Integral Equations

Regularity for nonisotropic two-phase problems with Lipschitz free boundaries

Mikhail Feldman

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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.

Article information

Source
Differential Integral Equations, Volume 10, Number 6 (1997), 1171-1179.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367438227

Mathematical Reviews number (MathSciNet)
MR1608061

Zentralblatt MATH identifier
0940.35047

Subjects
Primary: 35R35: Free boundary problems
Secondary: 35J15: Second-order elliptic equations 35R05: Partial differential equations with discontinuous coefficients or data 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]

Citation

Feldman, Mikhail. Regularity for nonisotropic two-phase problems with Lipschitz free boundaries. Differential Integral Equations 10 (1997), no. 6, 1171--1179. https://projecteuclid.org/euclid.die/1367438227


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