Partially overdetermined elliptic boundary value problems |
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Authors: | Ilaria Fragalà |
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Affiliation: | Dipartimento di Matematica del Politecnico, Piazza L. da Vinci, 20133 Milano, Italy |
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Abstract: | We consider semilinear elliptic Dirichlet problems in bounded domains, overdetermined with a Neumann condition on a proper part of the boundary. Under different kinds of assumptions, we show that these problems admit a solution only if the domain is a ball. When these assumptions are not fulfilled, we discuss possible counterexamples to symmetry. We also consider Neumann problems overdetermined with a Dirichlet condition on a proper part of the boundary, and the case of partially overdetermined problems on exterior domains. |
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Keywords: | 35J70 35B50 |
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