Ukrainian Mathematical Bulletin

Volume 3, Issue 3, 2006 pp. 339-359.

H\"older Regularity for the Gradients of Solutions of Degenerate Parabolic Systems

Authors: Gary M. Lieberman
Author institution: Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA, lieb@iastate.edu

Summary: We study a class of parabolic systems of the form $v_t=\mbox{div} (F(|Dv|Dv)$. The function $F$ satisfies a few technical hypotheses which are satisfied, for example, by $F(s)=s^{p-2}$ with $p>1$. Hence our results extend the standard results for the parabolic $p$-Laplacian operator. The method of proof is similar to the usual one but uses some new ideas about Poincar\'e-type inequalities and a special Gehring inequality.

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