Displaying similar documents to “On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.”

Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents

Lingeshwaran Shangerganesh, Arumugam Gurusamy, Krishnan Balachandran (2017)

Communications in Mathematics

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In this work, we study the existence and uniqueness of weak solutions of fourth-order degenerate parabolic equation with variable exponent using the difference and variation methods.

Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

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.

Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations

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.