Inversion of some two-dimensional integral equations
The author considers the integral equation \[ (1)\quad \iint_{S}(\gamma (\xi)/| x-\xi |^{1+\nu})d_{\xi}S=g(x),\quad x\in S,\quad 0\leq \nu \leq 2,\quad \nu \neq 1, \] where \(\gamma\) is unknown function, \(g\in L^ 2\), S is a plane domain. He obtains the solution of (1) by quadrature, when S is a halfplane or a disk. Classes of functions \(\gamma\) and g for which the solution is unique are indicated.
scientific article; zbMATH DE number 3960227
scientific article