The Journal of Geometric Analysis

, Volume 13, Issue 4, pp 715–738

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

  • Pei-Yong Wang

DOI: 10.1007/BF02921886

Cite this article as:
Wang, PY. J Geom Anal (2003) 13: 715. doi:10.1007/BF02921886


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 

Copyright information

© Mathematica Josephina, Inc. 2003

Authors and Affiliations

  • Pei-Yong Wang
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSanta Barbara

Personalised recommendations