We study the nonstationary boundary-value problem for the Poisson equation in a plane corner with a dynamic boundary condition on the one part of the corner and the Dirichlet condition on the other part. We prove one-to-one solvability of the problem in weighted Hölder spaces and obtain the corresponding coercive estimates. These estimates will be useful to solve a free boundary problem.
"On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner." Adv. Differential Equations 12 (10) 1167 - 1200, 2007.