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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 2 / ) 2 ( , 2 λ λ + + Η . 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. MSC 2010: 35K20

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