For a strictly convex set K subset of R-2 of class C-2 we consider its associated sub-Finsler K-perimeter vertical bar partial derivative E vertical bar(K) in H-1 and the prescribed mean curvature functional vertical bar partial derivative E vertical bar(K) - integral(E) f associated to a continuous function f . Given a critical set for this functional with Euclidean Lipschitz and intrinsic regular boundary, we prove that their characteristic curves are of class C-2 and that this regularity is optimal. The result holds in particular when the boundary of E is of class C-1. (C) 2021 The Authors. Published by Elsevier Inc.

Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group H^1 / Giovannardi, G; Ritore, M. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - ELETTRONICO. - 302:(2021), pp. 474-495. [10.1016/j.jde.2021.08.040]

Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group H^1

Giovannardi, G;
2021

Abstract

For a strictly convex set K subset of R-2 of class C-2 we consider its associated sub-Finsler K-perimeter vertical bar partial derivative E vertical bar(K) in H-1 and the prescribed mean curvature functional vertical bar partial derivative E vertical bar(K) - integral(E) f associated to a continuous function f . Given a critical set for this functional with Euclidean Lipschitz and intrinsic regular boundary, we prove that their characteristic curves are of class C-2 and that this regularity is optimal. The result holds in particular when the boundary of E is of class C-1. (C) 2021 The Authors. Published by Elsevier Inc.
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474
495
Giovannardi, G; Ritore, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1284583
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