Parabolic initial boundary value problems in nonsmooth cylinders with data in anisotropic Besov spaces (Q862060)

The authors prove sharp well-posedness results for the heat equation in arbitrary Lipschitz cylinders, when the boundary data are in parabolic Besov spaces and zero initial conditions. These results are proved by using the method of layer potentials extending \textit{R. M. Brown}'s ones in [Trans. Am. Math. Soc. 320, No. 1, 1--52 (1990; Zbl 0714.35037)].