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Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations
-
Pengfei Guan
and
Xu Lu
Published/Copyright:
April 3, 2012
Abstract
We establish a global geometric lower bound for the second fundamental form of the level surfaces of solutions to F(D2u, Du, u, x) = 0 in convex ring domains, in terms of boundary geometry and the structure of the elliptic operator F. We also prove a microscopic constant rank theorem, under a general structural condition introduced by Bianchini–Longinetti–Salani in 2009.
Received: 2010-10-28
Revised: 2011-09-24
Published Online: 2012-04-03
Published in Print: 2013-06
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces
- On nonary cubic forms: IV
- Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations
- Inhomogeneous cubic congruences and rational points on del Pezzo surfaces
- A reduction theorem for the Alperin–McKay conjecture
- Regularity of solutions to the parabolic fractional obstacle problem
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