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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 249, Pages 20–39
(Mi znsl578)
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This article is cited in 8 scientific papers (total in 8 papers)
On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth
A. A. Arkhipova Saint-Petersburg State University
Abstract:
We consider quasilinear nondiagonal parabolic systems with quadratic growth on the gradient in a parabolic cylinder $Q$. Under Dirichlet and Neumann boundary conditions partial Hölder continuity up to the lateral surface of $Q$ of solutions $u\in W_2^{1,1} (Q)\cap L^\infty(Q)$ is proved. Hausdorff dimension of a singular set is estimated. In the proof we get of the maximum principle theorem for corresponding model linear problems.
Received: 05.05.1997
Citation:
A. A. Arkhipova, “On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth”, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Zap. Nauchn. Sem. POMI, 249, POMI, St. Petersburg, 1997, 20–39; J. Math. Sci. (New York), 101:5 (2000), 3385–3397
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https://www.mathnet.ru/eng/znsl578 https://www.mathnet.ru/eng/znsl/v249/p20
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Abstract page: | 174 | Full-text PDF : | 73 |
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