Journal of Evolution Equations

, Volume 7, Issue 3, pp 415–428

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

Article

DOI: 10.1007/s00028-007-0278-y

Cite this article as:
Byun, SS. J. evol. equ. (2007) 7: 415. doi:10.1007/s00028-007-0278-y

Abstract.

This work treats Lp 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, 35R35Secondary 35J15, 35J25

Keywords:

Parabolic equationsBMO SpaceParabolic maximal functionRegularity theory

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesSeoul National UniversitySeoulKorea