On boundary and initial values of solutions of a second-order parabolic equation that degenerate on the domain boundary

Abstract

Properties of the solutions of a parabolic equation in the case of a Keldysh-type degeneracy on the boundary of the domain are investigated. The unique solvability of the first mixed problem for this equation is studied. Necessary and sufficient conditions for the existence of limits of the solution on the lateral surface of a cylindrical domain and on its lower base in L₂-type spaces are found.