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.
Starshapdness of level sets of solutions to elliptic equations / P. SALANI. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 84 (12):(2005), pp. 1185-1197.
Starshapdness of level sets of solutions to elliptic equations
SALANI, PAOLO
2005
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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