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Beschreibung:
We prove that nonsmooth quasilinear parabolic systems admit a local, strongly differentiable (with respect to time) solution in Lp over a bounded three-dimensional polyhedral space domain. The proof rests essentially on new elliptic regularity results for polyhedral Laplace interface problems with anisotropic materials. These results are based on sharp pointwise estimates for Green's function, which are also of independent interest. To treat the nonlinear problem, we then apply a classical theorem of Sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results. As applications we have in mind primarily reaction diffusion systems. The treatment of such equations in an Lp context seems to be new and allows (by Gauss' theorem) to define properly the normal component of currents across the boundary.