On the Hölder Continuity of Bounded Weak Solutions of Quasilinear Parabolic Systems.
Michael Struwe (1981)
Manuscripta mathematica
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Michael Struwe (1981)
Manuscripta mathematica
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D. G. Aronson, P. Besala (1967)
Colloquium Mathematicae
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J. Chabrowski (1972)
Colloquium Mathematicae
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Dmitry Portnyagin (2003)
Annales Polonici Mathematici
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A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.
Ivanov, Alexander V.
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H. Marcinkowska (1983)
Annales Polonici Mathematici
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P. Besala (1963)
Colloquium Mathematicae
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B. H. Gilding (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Tuomo Kuusi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
Andrzej W. Turski (1991)
Annales Polonici Mathematici
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H. Ugowski (1971)
Annales Polonici Mathematici
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Changchun Liu, Jinyong Guo (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.