Well-posedness of Neumann-type Elliptic Overdetermined Problem with Integral Condition

Abstract

The current paper is devoted to overdetermined elliptic problem with integral condition for derivatives. This overdetermined problem is converted to auxiliary nonlocal boundary value problem (ANBVP) with integral boundary condition. Well-posedness of abstract problem is established. Then, obtained results are used to obtain stability inequalities for solution of three Neumann-type inverse elliptic problems with integral condition to multidimensional differential equation.