We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body K0⊆R2n, for t-graphs on a bounded domain Ω in the Heisenberg group Hn. When the prescribed datum H is constant and strictly smaller than the Finsler mean curvature of ∂Ω, we prove the existence of a Lipschitz solution to the Dirichlet problem for the sub-Finsler CMC equation by means of a Finsler approximation scheme.
The prescribed mean curvature equation for t-graphs in the sub-Finsler Heisenberg group Hn / Giovannardi, Gianmarco; Pinamonti, Andrea; Pozuelo, Julián; Verzellesi, Simone. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 2024, 451:(2024), pp. 10978801-10978843. [10.1016/j.aim.2024.109788]
The prescribed mean curvature equation for t-graphs in the sub-Finsler Heisenberg group Hn
Giovannardi, Gianmarco;Pinamonti, Andrea
;Verzellesi, Simone
2024-01-01
Abstract
We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body K0⊆R2n, for t-graphs on a bounded domain Ω in the Heisenberg group Hn. When the prescribed datum H is constant and strictly smaller than the Finsler mean curvature of ∂Ω, we prove the existence of a Lipschitz solution to the Dirichlet problem for the sub-Finsler CMC equation by means of a Finsler approximation scheme.| File | Dimensione | Formato | |
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