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arXiv · 2201.09605

An inequality for the normal derivative of the Lane-Emden ground state

Rupert L. Frank·Simon Larson
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Abstract

We consider Lane-Emden ground states with polytropic index $0\leq q-1\leq 1$, that is, minimizers of the Dirichlet integral among $L^q$-normalized functions. Our main result is a sharp lower bound on the $L^2$-norm of the normal derivative in terms of the energy, which implies a corresponding isoperimetric inequality. Our bound holds for arbitrary bounded open Lipschitz sets $\Omega\subset\mathbb{R}^d$, without assuming convexity.

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Rupert L. Frank, Simon Larson. 2022-01-24. An inequality for the normal derivative of the Lane-Emden ground state. https://arxiv.org/abs/2201.09605

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