One-dimensional symmetry for the solutions of a three-dimensional water wave problem
Analysis of PDEs
2017-10-27 v2
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 an article by De La Llave and the third author. In this paper, a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument.
Keywords
Cite
@article{arxiv.1710.01137,
title = {One-dimensional symmetry for the solutions of a three-dimensional water wave problem},
author = {Eleonora Cinti and Pietro Miraglio and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1710.01137},
year = {2017}
}