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Mathematics > Analysis of PDEs
Title: Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations
(Submitted on 7 Apr 2010 (v1), last revised 10 Oct 2010 (this version, v2))
Abstract: We establish a geometric lower bound for the principal curvature of the level surfaces of solutions to $F(D^2u, Du, u, x)=0$ in convex ring domains, under a refined structural condition introduced by Bianchini-Longinetti-Salani in \cite{BLS}. We also prove a constant rank theorem for the second fundamental form of the convex level surfaces of these solutions.
Submission history
From: Pengfei Guan [view email][v1] Wed, 7 Apr 2010 21:07:06 GMT (18kb)
[v2] Sun, 10 Oct 2010 15:12:28 GMT (20kb)
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