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arXiv · 1710.03140

Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

Francesco Della Pietra·Giuseppina di Blasio·Nunzia Gavitone
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Abstract

In this paper we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue $\lambda_{F}(p,\Omega)$ of the anisotropic $p$-Laplacian, $1<p<+\infty$. Our aim is to enhance how, by means of the $\mathcal P$-function method, it is possible to get several sharp estimates for $\lambda_{F}(p,\Omega)$ in terms of several geometric quantities associated to the domain. The $\mathcal P$-function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient.

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Francesco Della Pietra, Giuseppina di Blasio, Nunzia Gavitone. 2017-10-09. Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle. https://arxiv.org/abs/1710.03140

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