2005-10-20Buch DOI: 10.18452/2516
A Global Lp-Gradient Estimate on Weak Solutions of Nonlinear Parabolic Systems under Mixed Boundary Conditions
In this paper, we prove the integrability of the spatial gradient Du to an exponent p>2 near the boundary, u being a weak solution of a nonlinear parabolic system under mixed boundary conditions. Our method of proof relies on an adaption of a technique by Gehring-Giaquinta-Modica (higher integrability by reverse Hölder inequality) to cubes which possibly intersect a hyperplane. Combined with the interior estimate in (Naumann, J., Wolff, M.: Interior integral estimates on weak solutions of nonlinear parabolic systems. - Preprint no. 94-12; Fachber. Math., Humboldt-Univ.) we obtain a global Lp-gradient estimate.
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