Calculus of Variations and Geometric Measure Theory
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A. Farina - E. Valdinoci

On partially and globally overdetermined problems of elliptic type

created by farina on 14 Feb 2013

[BibTeX]

Accepted Paper

Inserted: 14 feb 2013
Last Updated: 14 feb 2013

Journal: American Journal of Mathematics
Year: 2012

Abstract:

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 classi cation of the solution and of the domain. In particular, we fi nd 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 fi nd the shape of the admissible domains. Models of this type arise in several areas of mathematical physics and shape optimization.


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