We consider the homogeneous Dirichlet problem Delta u = -f (u) <= 0 in Omega with u = 0 on delta Omega. We are interested in the inverse problem of determining the nonlinear source f from knowledge of the normal derivative of u, partial derivative u/partial derivative n, on an open arc Gamma of partial derivative. It is well known that this fails if Omega is a ball. On the other hand, Beretta and Vogelius proved that an analytic source f is uniquely determined from knowledge of (partial derivative u/partial derivative n)vertical bar Gamma if Gamma has at least a true corner. In this paper we try to bridge the gap finding a class of smooth domains for which the determination of analytic f is possible.

Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains / E. BERETTA; S. VESSELLA. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 135A:(2005), pp. 267-283.

Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains

VESSELLA, SERGIO
2005

Abstract

We consider the homogeneous Dirichlet problem Delta u = -f (u) <= 0 in Omega with u = 0 on delta Omega. We are interested in the inverse problem of determining the nonlinear source f from knowledge of the normal derivative of u, partial derivative u/partial derivative n, on an open arc Gamma of partial derivative. It is well known that this fails if Omega is a ball. On the other hand, Beretta and Vogelius proved that an analytic source f is uniquely determined from knowledge of (partial derivative u/partial derivative n)vertical bar Gamma if Gamma has at least a true corner. In this paper we try to bridge the gap finding a class of smooth domains for which the determination of analytic f is possible.
2005
135A
267
283
E. BERETTA; S. VESSELLA
File in questo prodotto:
File Dimensione Formato  
PROC_Ed_Beretta_V.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 180.29 kB
Formato Adobe PDF
180.29 kB Adobe PDF   Richiedi una copia

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

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/225923
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact