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2005-10-20Buch DOI: 10.18452/2516
A Global Lp-Gradient Estimate on Weak Solutions of Nonlinear Parabolic Systems under Mixed Boundary Conditions
Naumann, Joachim
Wolff, Michael
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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DOI
10.18452/2516
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