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

Eleonora Cinti, Pietro Miraglio, Enrico Valdinoci

Research output: Contribution to journalArticle

Abstract

We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimensions 2 and 3. More precisely, we prove that stable solutions in dimension 2 and minimizers and monotone solutions in dimension 3 depend on only one Euclidean variable. Monotone solutions in the 2-dimensional case without weights were studied in de la Llave and Valdinoci (Math Res Lett 16(5):909–918, 2009). In our paper, a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument.

Original languageEnglish
JournalJournal of Geometric Analysis
DOIs
Publication statusE-pub ahead of print - 17 Sep 2019

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