We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimension 3. More precisely we prove that minimizers and bounded monotone solutions depend on only one Euclidean variable. The analogue of this result for the 2-dimensional case (and without weights) was established in 16. In this paper a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument.

One-Dimensional Symmetry for the Solutions of a Three-Dimensional Water Wave Problem

Cinti E.;Valdinoci E.
2020

Abstract

We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimension 3. More precisely we prove that minimizers and bounded monotone solutions depend on only one Euclidean variable. The analogue of this result for the 2-dimensional case (and without weights) was established in 16. In this paper a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument.
Cinti E.; Miraglio P.; Valdinoci E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/707210
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