Article

The Journal of Geometric Analysis

, Volume 13, Issue 4, pp 715-738

First online:

Existence of solutions of Two-Phase free boundary problems for fully nonlinear elliptic equations of second order

  • Pei-Yong WangAffiliated withDepartment of Mathematics, University of California

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Abstract

In this article, we have established existence of a solution to the 2 -phase free boundary problem for some fully nonlinear elliptic equations and also shown the free boundary has finite Hn−1 Hausdorff measure and a normal in a measuretheoretic sense Hn−1 almost everywhere. The regularity theory developed in [9] and [10] for this free boundary problem then leads to the fact that the free boundary is locally a C1,α surface near Hn−1-a.e. point.

Math Subject Classifications

35R35 35J60 28A78 49Q15

Key Words and Phrases

Free boundary two-phase fully nonlinear elliptic equations Hausdorff measure