A modern proof of the Maximum Principle

Andrzej W. Turski

Displaying similar documents to “A modern proof of the Maximum Principle”

A generalization of the maximum principle to nonlinear parabolic systems

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.

Uniqueness of positive weak solutions of second order parabolic equations

D. G. Aronson (1965)

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Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents

Lingeshwaran Shangerganesh, Arumugam Gurusamy, Krishnan Balachandran (2017)

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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.

On the Hölder Continuity of Bounded Weak Solutions of Quasilinear Parabolic Systems.

Michael Struwe (1981)

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Uniqueness of positive solutions of parabolic equations with unbounded coefficients

D. G. Aronson, P. Besala (1967)

Colloquium Mathematicae

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Evaluations of solutions of a second order parabolic equation

P. Besala (1963)

Colloquium Mathematicae

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A maximum principle for nonlinear parabolic equations

D. G. Aronson, James Serrin (1967)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On behaviour of non-negative weak solutions of parabolic equations at the boundary

J. Chabrowski (1972)

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Maximum principles for parabolic systems coupled in both first-order and zero-order terms.

Zhou, Chiping (1994)

International Journal of Mathematics and Mathematical Sciences

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Regularity for doubly nonlinear parabolic equations

Ivanov, Alexander V.

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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.