Frank, Rupert L. and Larson, Simon (2022) An inequality for the normal derivative of the Lane-Emden ground state. Advances in Calculus of Variations . ISSN 1864-8258. doi:10.1515/acv-2022-0005. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20221019-344256700.16
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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.
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| 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. | ||||||||
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| DOI: | 10.1515/acv-2022-0005 | ||||||||
| Record Number: | CaltechAUTHORS:20221019-344256700.16 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20221019-344256700.16 | ||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 117498 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | Research Services Depository | ||||||||
| Deposited On: | 27 Oct 2022 22:00 | ||||||||
| Last Modified: | 27 Oct 2022 22:00 |
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