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

Frank, Rupert L. und 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 1864-8258
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 390814868