Solution of one initial-boundary Wentzel problem for a parabolic equation with discontinuous coefficients by the boundary integral equation method

In this article we consider the question of existence in the Holder class of the solution of the initial-boundary problem for a linear parabolic second-degree equation with discontinuous coefficients in noncylindrical domain. This domain is bounded of the smooth elementary surfaces of the Holder class H ^{2+λ, (2+λ )/2}. The boundary conditions and the conjugation condition of the Wentzel type are given to external and internal boundaries of a domain respectively. We use the potential method to solve this problem.