We extend the symmetry result of Gidas-Ni-Nirenberg to semilinear polyharmonic Dirichlet problems in the unit ball. In the proof we develop a new variant of the method of moving planes relying on fine estimates for the Green function of the polyharmonic operator. We also consider minimizers for subcritical higher order Sobolev embeddings. For embeddings into weighted spaces with a radially symmetric weight function, we show that the minimizers are at least axially symmetric. This result is sharp since we exhibit examples of minimizers which do not have full radial symmetry.

Radial symmetry of positive solutions in nonlinear polyharmonic Dirichlet problems / Berchio, Elvise; Gazzola, F.; Weth, T.. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 620:(2008), pp. 165-183. [10.1515/CRELLE.2008.052]

Radial symmetry of positive solutions in nonlinear polyharmonic Dirichlet problems

BERCHIO, ELVISE;
2008

Abstract

We extend the symmetry result of Gidas-Ni-Nirenberg to semilinear polyharmonic Dirichlet problems in the unit ball. In the proof we develop a new variant of the method of moving planes relying on fine estimates for the Green function of the polyharmonic operator. We also consider minimizers for subcritical higher order Sobolev embeddings. For embeddings into weighted spaces with a radially symmetric weight function, we show that the minimizers are at least axially symmetric. This result is sharp since we exhibit examples of minimizers which do not have full radial symmetry.
File in questo prodotto:
File Dimensione Formato  
Berchio 7.pdf

non disponibili

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 159.03 kB
Formato Adobe PDF
159.03 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2522500
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo