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

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)

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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.

Item Type:Article
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URLURL TypeDescription
Frank, Rupert L.0000-0001-7973-4688
Larson, Simon0000-0002-0057-8211
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.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Knut and Alice Wallenberg FoundationKAW 2021.0193
Record Number:CaltechAUTHORS:20221019-344256700.16
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ID Code:117498
Deposited By: Research Services Depository
Deposited On:27 Oct 2022 22:00
Last Modified:27 Oct 2022 22:00

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