Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. In fact, we show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric.
Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration / G. Ciraolo; R. Magnanini; S. Sakaguchi. - In: JOURNAL D'ANALYSE MATHEMATIQUE. - ISSN 0021-7670. - STAMPA. - 128:(2016), pp. 337-353. [10.1007/s11854-016-0011-2]
Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration
MAGNANINI, ROLANDO;
2016
Abstract
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. In fact, we show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric.File | Dimensione | Formato | |
---|---|---|---|
ReprintJAM2016.pdf
Open Access dal 17/03/2017
Descrizione: Articolo principale
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
204.96 kB
Formato
Adobe PDF
|
204.96 kB | Adobe PDF | |
CiraoloMagnaniniSakaguchiArx1307.1257.pdf
accesso aperto
Descrizione: Articolo principale
Tipologia:
Altro
Licenza:
Tutti i diritti riservati
Dimensione
216.13 kB
Formato
Adobe PDF
|
216.13 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.