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Hölder Continuity of Weak Solutions for Parabolic Equations with Nonstandard Growth Conditions

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Abstract

In this paper, we investigate the interior regularity including the local boundedness and the interior Hölder continuity of weak solutions for parabolic equations of the p(x, t)–Laplacian type. We improve the Moser iteration technique and generalize the known results for the elliptic problem to the corresponding parabolic problem.

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Correspondence to Meng Xu.

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Xu, M., Chen, Y.Z. Hölder Continuity of Weak Solutions for Parabolic Equations with Nonstandard Growth Conditions. Acta Math Sinica 22, 793–806 (2006). https://doi.org/10.1007/s10114-005-0582-9

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