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Starshapedness of Level Sets for Solutions of Nonlinear Elliptic Equations

✍ Scribed by Elisa Francini

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
277 KB
Volume
193
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We introduce a measure for the starshapedness of the level sets of solutions of certain nonlinear elliptic equations in a starshaped ring Ξ© of IR^n^. We prove that a function which characterizes the starshapedness does not attain its minimum in Ξ©.

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## Abstract Given a __C__^2^ function __u__, we consider its quasi–convex envelope __u__\* and we investigate the relationship between __D__^2^__u__ and __D__^2^__u__\* (the latter intended in viscosity sense); we obtain two inequalities between the tangential Laplacian of __u__ and __u__\* and the