The boundary-value problems for parabolic equations with a nonlocal condition and degenerations

摘要

With the help of the principle of maximum and the a priori estimates, we consider the first boundary-value problem and the problem with directional derivative under a nonlocal condition in the time variable for parabolic equations with power singularities of the coefficients in the time and space variables. The existence and the uniqueness of solutions of the posed problems are proved for the Holder spaces with power weight.