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Hölder regularity for the general parabolic p(x, t)-Laplacian equations

  • Fengping Yao
Article

Abstract

In this paper we obtain the local Hölder regularity of the gradient of weak solutions for the general parabolic p(x, t)-Laplacian equations
$$u_t-\text{div}\ \mathcal{A}\left( \nabla u, x, t \right)\,=\,\text{div} \left(|\mathrm{\bf f}|^{p(x, t)-2} \mathrm{\bf f}\right),$$
provided p(x, t), \({\mathcal{A}}\) and \({\mathrm{\bf f}}\) satisfy some proper conditions. More precisely, we shall prove that
$$\nabla u \in C_{loc}^{0;\alpha,\alpha/2}(\Omega_T)\,\mbox{for some} \, \, \alpha \in (0, 1). $$

Mathematics Subject Classification (2010)

35K55 35K65 

Keywords

Hölder Regularity Gradient Divergence Parabolic p(x, t)-Laplacian 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina

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