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.; Miraglio P.; Valdinoci E.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 30:2(2020), pp. 1804-1835. [10.1007/s12220-019-00279-z]
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.File | Dimensione | Formato | |
---|---|---|---|
WW-2019.pdf
accesso aperto
Tipo:
Preprint
Licenza:
Licenza per accesso libero gratuito
Dimensione
394.36 kB
Formato
Adobe PDF
|
394.36 kB | Adobe PDF | Visualizza/Apri |
WW-FIN.pdf
accesso aperto
Tipo:
Postprint
Licenza:
Licenza per accesso libero gratuito
Dimensione
577.96 kB
Formato
Adobe PDF
|
577.96 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.