Mathematical Research Letters

Volume 21 (2014)

Number 5

Symmetry minimizes the principal eigenvalue: an example for the Pucci’s sup-operator

Pages: 953 – 967

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n5.a3

Authors

Isabeau Birindelli (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

Fabiana Leoni (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

Abstract

We explicitly evaluate the principal eigenvalues of the extremal Pucci’s sup-operator for a class of planar domains, and we prove that, for fixed area, the eigenvalue is minimal for the most symmetric set.

Keywords

Pucci’s extremal operators, principal eigenvalue, principal eigenfunction, symmetry

2010 Mathematics Subject Classification

35J60

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Published 9 December 2014