Journal of Evolution Equations

, Volume 7, Issue 3, pp 415–428 | Cite as

Optimal W1,p regularity theory for parabolic equations in divergence form

Article

Abstract.

This work treats L p regularity theory for weak solutions of parabolic equations in divergence form with discontinuous coefficients on nonsmooth domains. We essentially obtain an optimal condition on the coefficients under which the global W1,p regularity theory holds.

Mathematics Subject Classifications (2000):

Primary 35R05, 35R35 Secondary 35J15, 35J25 

Keywords:

Parabolic equations BMO Space Parabolic maximal function Regularity theory 

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Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesSeoul National UniversitySeoulKorea

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