A regularity result for quasilinear parabolic systems |
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Authors: | Michael Pingen |
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Institution: | 1.Fachbereich Mathematik,Universit?t Duisburg-Essen,Duisburg,Germany |
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Abstract: | We consider bounded, weak solutions of certain quasilinear parabolic systems of second order. If the solution fulfills a suitable
smallness condition, we show that it is H?lder continuous and satisfies an a priori estimate. This is a well known result
of Giaquinta and Struwe 3]. Their argument employs the use of Green’s functions, which is completely avoided in our proof.
Instead, our crucial tool is a weak Harnack inequality for supersolutions due to Trudinger 7] in connection with a technique
developed by L.Caffarelli 1].
Received: 25 September 2006 |
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Keywords: | 35K40 35D10 |
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