An inequality for the normal derivative of the Lane-Emden ground state
Journal article, 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
Author
Rupert L. Frank
California Institute of Technology (Caltech)
Ludwig Maximilian University of Munich (LMU)
MCQST
Simon Larson
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Advances in Calculus of Variations
1864-8258 (ISSN) 18648266 (eISSN)
Vol. 17 2 255-276Subject Categories
Computational Mathematics
Theoretical Chemistry
Mathematical Analysis
DOI
10.1515/acv-2022-0005