An inequality for the normal derivative of the Lane-Emden ground state
Artikel i vetenskaplig tidskrift, 2024
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.
Brunn-Minkowski
normal derivative
Lane-Emden
Författare
Rupert L. Frank
California Institute of Technology (Caltech)
Ludwig-Maximilians-Universität München (LMU)
MCQST
Simon Larson
Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori
Göteborgs universitet
Advances in Calculus of Variations
1864-8258 (ISSN) 18648266 (eISSN)
Vol. 17 2 255-276Ämneskategorier
Beräkningsmatematik
Teoretisk kemi
Matematisk analys
DOI
10.1515/acv-2022-0005