Full regularity for a class of degenerated parabolic systems in two spatial variables |
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| Authors: | J Frehse G A Seregin |
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| Institution: | (1) Institut für Angewandte Mathematik, Abteilung für Angewandte Analysis, Beringstr. 6, D-53115 Bonn, Germany. E-mail: erdbeere@iam.uni-bonn.de, DE;(2) Steklov Institute of Mathematics, Fontanka 27, 191011 St. Petersburg, Russia. E-mail: seregin@pdmi.ras.ru, RU |
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| Abstract: | The authors consider quasilinear parabolic systems in two space dimensions. The function a has p-growth behaviour, 1< p < ∞, and the ellipticity “constant” behaves like (1+|∇u|)
p
− 2. The author prove full regularity of the weak solution on interior subdomains, but globally in time. The key idea in the
proof is a technique to obtain boundedness of the gradient based on logarithmic estimates.
Received: 8 July 1998 / Revised version: 19 February 1999 |
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| Keywords: | Mathematics Subject Classification (1991): 35B65 35D10 35K55 |
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