We consider some elliptic pde's with Dirichlet and Neumann data prescribed on some portion of the boundary of the domain and we obtain rigidity results that give a classification of the solution and of the domain. In particular, we find mild conditions under which a partially overdetermined problem is, in fact, globally overdetermined: this enables us to use several classical results in order to classify all the domains that admit a solution of suitable, general, partially overdetermined problems. These results may be seen as solutions of suitable inverse problems-that is to say, given that an overdetermined system possesses a solution, we find the shape of the admissible domains. Models of this type arise in several areas of mathematical physics and shape optimization.
|Titolo:||On partially and globally overdetermined problems of elliptic type|
VALDINOCI, ENRICO (Ultimo)
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1353/ajm.2013.0052|
|Appare nelle tipologie:||01 - Articolo su periodico|