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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 C 1,α
Author(s) -
Wang PeiYong
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200007)53:7<799::aid-cpa1>3.0.co;2-q
Subject(s) - mathematics , lipschitz continuity , nonlinear system , free boundary problem , mathematical analysis , order (exchange) , boundary (topology) , boundary value problem , elliptic curve , lipschitz domain , extension (predicate logic) , physics , finance , quantum mechanics , computer science , economics , programming language
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. © 2000 John Wiley & Sons, Inc.