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Regularity of free boundaries of two-phase problems for fully nonlinear elliptic equations of second order I. Lipschitz free boundaries are C1,α

✍ Scribed by Pei-Yong Wang

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 91 KB
Volume: 53
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(200007)53:7<799::aid-cpa1>3.0.co;2-q

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✦ Synopsis

In this paper, we study an extension of a C 1,α regularity theory developed by L. Caffarelli in [2] to some fully nonlinear elliptic equations of second order. In fact, we investigate a two-phase free boundary problem in which a fully nonlinear elliptic equation of second order is verified by the solution in the positive and the negative domains. Assuming the free boundary is locally a Lipschitz graph, we have established the C 1,α regularity of the free boundary.