The Faber-Krahn inequality states that balls are the unique minimizers of the first eigenvalue of the p-Laplacian among all sets with a fixed volume. In this paper we prove a sharp quantitative form of this inequality. This extends to the case p>1 a recent result proved by L. Brasco, G. De Philippis and B. Velichkov [Duke Math. J., 2015] for the Laplacian.
A quantitative form of Faber-Krahn inequality / Fusco, Nicola; Zhang Yi, Ru-Ya. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 56:5(2017), pp. 1-44. [10.1007/s00526-017-1224-7]
A quantitative form of Faber-Krahn inequality
Fusco Nicola;
2017
Abstract
The Faber-Krahn inequality states that balls are the unique minimizers of the first eigenvalue of the p-Laplacian among all sets with a fixed volume. In this paper we prove a sharp quantitative form of this inequality. This extends to the case p>1 a recent result proved by L. Brasco, G. De Philippis and B. Velichkov [Duke Math. J., 2015] for the Laplacian.File in questo prodotto:
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