Symmetry in Multi-Phase Overdetermined Problems

Babaoglu C., Shahgholian H.

JOURNAL OF CONVEX ANALYSIS, cilt.18, sa.4, ss.1013-1024, 2011 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 4
  • Basım Tarihi: 2011
  • Dergi Adı: JOURNAL OF CONVEX ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1013-1024
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

In this paper we prove symmetry for a multi-phase overdetermined problem, with nonlinear governing equations. The most simple form of our problem (in the two-phase case) is as follows: For a bounded C-1 domain Omega subset of R-n (n >= 2) let u(+) be the Green's function (for the p-Laplace operator) with pole at some interior point (origin, say), and u(-) the Green's function in the exterior with pole at infinity. If for some strictly increasing function F(t) (with some growth assumption) the condition partial derivative(v)u(+) = F(partial derivative(v)u(-)) holds on the boundary partial derivative Omega, then Omega is necessarily a ball. We prove the more general multi-phase analog of this problem.