Published October 27, 2022
| public
Journal Article
An inequality for the normal derivative of the Lane-Emden ground state
- Creators
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Frank, Rupert L.
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Larson, Simon
Chicago
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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 L²-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 Ω ⊂ ℝᵈ, without assuming convexity.
Additional Information
Funding statement: Partial support through U.S. National Science Foundation grant DMS-1954995 (R. L. Frank), through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868 (R. L. Frank), and through Knut and Alice Wallenberg Foundation grant KAW 2021.0193 (S. Larson) is acknowledged. The authors would like to thank the anonymous referee for helpful suggestions.Additional details
- Eprint ID
- 117498
- Resolver ID
- CaltechAUTHORS:20221019-344256700.16
- NSF
- DMS-1954995
- Deutsche Forschungsgemeinschaft (DFG)
- EXC-2111-390814868
- Knut and Alice Wallenberg Foundation
- KAW 2021.0193
- Created
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2022-10-27Created from EPrint's datestamp field
- Updated
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2022-10-27Created from EPrint's last_modified field