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July  2008, 20(3): 617-637. doi: 10.3934/dcds.2008.20.617

$W^{1,p}$ regularity for the conormal derivative problem with parabolic BMO nonlinearity in reifenberg domains

Sun-Sig Byun 1, and  Lihe Wang 2,

1. 

Department of Mathematical Sciences, Seoul National University, Seoul 151-747
2. 

Department of Mathematics, University of Iowa, Iowa City, IA 52242

Received  January 2007 Revised  July 2007 Published  December 2007

We obtain an optimal $W^{1,p}$, $2 \leq p < \infty$, regularity theory on the conormal derivative problem for a nonlinear parabolic equation in divergence form with small BMO nonlinearity in a $\delta$-Reifenberg flat domain.
Keywords: Parabolic maximal function, Conormal derivative problem, Nonlinear Parabolic Equation, BMO space, Reifenberg flat domain..
Mathematics Subject Classification: Primary 35R05, 35R35; Secondary 35J15, 35J2.
Citation: Sun-Sig Byun, Lihe Wang. $W^{1,p}$ regularity for the conormal derivative problem with parabolic BMO nonlinearity in reifenberg domains. Discrete & Continuous Dynamical Systems, 2008, 20 (3) : 617-637. doi: 10.3934/dcds.2008.20.617
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