A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation

  • Gao-Feng Zheng

    Department of Mathematics, Huazhong Normal University, Wuhan 430079, PR China

Abstract

A quasi-monotonicity formula for the solution to a semilinear parabolic equation , in with -Dirichlet boundary condition is obtained. As an application, it is shown that for some suitable global weak solution and any compact set there exists a close subset such that is continuous in and the -dimensional parabolic Hausdorff measure of is finite.

Cite this article

Gao-Feng Zheng, A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 6, pp. 1333–1360

DOI 10.1016/J.ANIHPC.2010.07.001