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Applicable Analysis
An International Journal
Volume 84, 2005 - Issue 12
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Original Articles

Starshapedness of level sets of solutions to elliptic PDEs

Paolo Salani *View further author information
Pages 1185-1197 | Received 01 Jan 2002, Accepted 02 Apr 2004, Published online: 04 Sep 2006
 
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Abstract

We investigate how some geometric properties of the domain are inherited by level sets of solutions of elliptic equations. In particular we prove that, under suitable assumptions, solutions of elliptic Dirichlet problems in starshaped rings have starshaped level sets. Our results are applicable to a large class of operators, including fully-nonlinear ones.

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Paolo Salani Footnote*

Email: [email protected]

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