We deal with Monge-Ampere type equations modeled upon general Finsler norms H in R^n. An overdetermined problem for convex solutions to these equations is analyzed. The relevant solutions are subject to both a homogeneous Dirichlet condition and a second boundary condition, designed on H, on the gradient image of the domain. The Wulff shape symmetry associated with H of the solutions is established.
Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Ampère equations / Cianchi A.; Salani P.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 285:(2023), pp. 0-0. [10.1016/j.jfa.2023.110091]
Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Ampère equations
Cianchi A.
;Salani P.
2023
Abstract
We deal with Monge-Ampere type equations modeled upon general Finsler norms H in R^n. An overdetermined problem for convex solutions to these equations is analyzed. The relevant solutions are subject to both a homogeneous Dirichlet condition and a second boundary condition, designed on H, on the gradient image of the domain. The Wulff shape symmetry associated with H of the solutions is established.
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