Parabolic problems and boundary integral equations

Here we consider initial boundary value problems for parabolic equations in non-bounded (with respect to time) domains by using the single-layer potential. We discuss the solvability in anisotropic Holder spaces of the boundary integral equations, to which original parabolic problems are reduced. We construct the special operators (regularizers) for these integral equations which transform them to equivalent integral Volterra equations of the second kind with weakly singular kernels. As a corollary we obtain the theorem about the classical solvability in anisotropic Holder spaces for initial boundary value parabolic problems. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.