An overdetermined problem for elliptic equations
Kalmenov T. Kakharman N.
2024American Institute of Mathematical Sciences
AIMS Mathematics
2024#9Issue 820627 - 20640 pp.
This paper is devoted to finding a necessary and sufficient condition for the solvability of the overdetermined problem for Poisson’s equation with both the Dirichlet and Neumann conditions on the entire boundary. The proof is based on the boundary condition formula for the Newton potential. The obtained results are also extended to general second-order linear elliptic equations. As a byproduct, we present a characterization of the Schiffer property. It gives a definitive answer to the Schiffer problem.
Dirichlet condition , Neumann condition , Newton potential , overdetermined problem , Schiffer conjecture
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Institute of Mathematics and Mathematical Modeling, Pushkin Str. 125, Almaty, 050010, Kazakhstan
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