Year: 2024
Type: article
Abstract: 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.
Source: AIMS Mathematics
Authors: Tynysbek Kalmenov, Nurbek Kakharman
Institution: Institute of Mathematics and Mathematical Modeling
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
Funder: Nazarbayev University
Award: G2586275074
OpenAlex ID: W4400019155