Let \Omega be an open connected subset of R^n for which the imbedding of the Sobolev space W^{1,2}_0(\Omega) into the space L^2(\Omega) is compact. We consider the Dirichlet eigenvalue problem for the Laplace operator in the open subset \phi(\Omega) of R^n, where \phi is a Lipschitz continuous homeomorphism of onto \phi(\Omega). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of \phi.
A real analyticity result for symmetric functions of the eigenvalues of a domain dependent Dirichlet problem for the Laplace operator
LAMBERTI, PIER DOMENICO;LANZA DE CRISTOFORIS, MASSIMO
2004
Abstract
Let \Omega be an open connected subset of R^n for which the imbedding of the Sobolev space W^{1,2}_0(\Omega) into the space L^2(\Omega) is compact. We consider the Dirichlet eigenvalue problem for the Laplace operator in the open subset \phi(\Omega) of R^n, where \phi is a Lipschitz continuous homeomorphism of onto \phi(\Omega). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of \phi.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
