On partially and globally overdetermined problems of elliptic type

Alberto Farina, Enrico Valdinoci

Research output: Contribution to journalArticle

19 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1699-1726
Number of pages28
JournalAmerican Journal of Mathematics
Issue number6
Publication statusPublished - 1 Jan 2013
Externally publishedYes


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