Calculus of Variations and Geometric Measure Theory
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E. Cinti - P. Miraglio - E. Valdinoci

One-dimensional symmetry for the solutions of a three-dimensional water wave problem

created by cinti on 04 Oct 2017


Submitted Paper

Inserted: 4 oct 2017
Last Updated: 4 oct 2017

Year: 2017


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.


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