Global gradient estimates for degenerate parabolic equations in nonsmooth domains |
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Authors: | Mikko Parviainen |
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Institution: | (1) Institute of Mathematics, Helsinki University of Technology, P. O. Box 1100, 02015 TKK, Finland |
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Abstract: | This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective
is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies
a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates
for the gradient. The results extend to the parabolic systems as well. The higher integrability estimates provide a useful
tool in several applications.
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Keywords: | Boundary value problem Gehring lemma Global higher integrability Initial value problem Reverse H?lder inequality |
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