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

Sun-Sig Byun; Lihe Wang

doi:10.3934/dcds.2008.20.617

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2008, Volume 20, Issue 3: 617-637. Doi: 10.3934/dcds.2008.20.617

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$W^{1,p}$ 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: December 31, 2006

Revised: June 30, 2007

Published: August 2008

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Abstract

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.

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Mathematics Subject Classification: Primary 35R05, 35R35; Secondary 35J15, 35J25.

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

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