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Maximum Principle for Nonlinear Parabolic Equations

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Abstract

A maximum principle is obtained for solutions of parabolic equations of the form

$$ \mathcal{L}u-{u}_t=f\left(x,t,u, Du\right), $$

where

$$ \mathcal{L}u=\sum \limits_{i,j}^n{a}_{ij}\left(x,t,u\right)\frac{\partial^2u}{\partial {x}_i\partial {x}_j}+\sum \limits_{i=1}^n{b}_i\left(x,t,u\right)\frac{\partial u}{\partial {x}_i}. $$

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. A. Kon’kov

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  1. A. A. Kon’kov
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Correspondence to A. A. Kon’kov.

Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 31, pp. 63–86, 2016.

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Kon’kov, A.A. Maximum Principle for Nonlinear Parabolic Equations. J Math Sci 234, 423–439 (2018). https://doi.org/10.1007/s10958-018-4020-9

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  • DOI: https://doi.org/10.1007/s10958-018-4020-9

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