We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.
Brandolini B., Nitsch C., Trombetti C. (2010). An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit. ARCHIV DER MATHEMATIK, 94(4), 391-400 [10.1007/s00013-010-0102-8].
An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit
Brandolini B.
;
2010-01-01
Abstract
We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.
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