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

Frank, Rupert L. and Larson, Simon (2022): An inequality for the normal derivative of the Lane-Emden ground state. In: Advances in Calculus of Variations

Abstract

We consider Lane-Emden ground states with polytropic index 0 <= q - 1 <= 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 of R-d, without assuming convexity.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Computer Science
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• ISSN: 1864-8258
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 390814868