Uniqueness of positive weak solutions of second order parabolic equations
D. G. Aronson (1965)
Annales Polonici Mathematici
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D. G. Aronson (1965)
Annales Polonici Mathematici
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M. Struwe, M. Giaquinta (1981)
Manuscripta mathematica
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J. Chabrowski (1972)
Colloquium Mathematicae
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Ivanov, Alexander V.
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Jana Stará, Oldřich John, Jan Malý (1986)
Commentationes Mathematicae Universitatis Carolinae
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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.
Dmitry Portnyagin (2008)
Applicationes Mathematicae
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Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.
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.
Horn, Werner (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Wolf von Wahl (1983)
Annales Polonici Mathematici
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