Well-posed problems for the Laplace operator in a punctured disk
Nonstandard boundary value problems are studied for the Poisson equation on a planar ball \(\Omega \). It is proved that if this problem has a unique stable solution, then there exists a continuous linear operator \(K\) from \(L^2 (\Omega )\) to \(W^{2,2}(\Omega )\) such that this problem takes the form \(\Delta u=f\) in \(\Omega \), \(u=K(f)\) on \(\partial \Omega \).
well-posed solvable boundary-value problem
scientific article; zbMATH DE number 5980830