We give a complete description of well-posed solvable boundary-value problems for the Laplace operator in the disk and in the punctured disk. We present formulas for resolvents of wellposed problems for the Laplace operator in the disk.

We study the Laplace operator in a punctured domain in a Hilbert space. We obtain an analog of the Green formula and a class of self-adjoint extensions of the Laplacian. We also investigate a certain class of well-posed problems.