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Local regularity of weak solutions to a class of parabolic systems with quadratic nonlinearities in the gradient

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Abstract

We consider quasilinear parabolic systems of equations with nondiagonal principal matrices and quadratic nonlinearities in the gradient. Under a one-side condition on the nonlinear terms, we study the local smoothness of the possibly unbounded weak solutions.

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Acknowledgements

The author’s research has been financially supported by the Russian Fond of the Basic Research (RFBR), Grant 20-01-00630a. The author thanks Professor Nina N. Uraltseva for her helpful remarks and advices.

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  1. Mathematical and Mechanical Faculty, Saint Petersburg State University, Universitetskaya nab.7/9, St. Petersburg, 199034, Russia

    Arina A. Arkhipova

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  1. Arina A. Arkhipova
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Arkhipova, A.A. Local regularity of weak solutions to a class of parabolic systems with quadratic nonlinearities in the gradient. manuscripta math. 170, 497–529 (2023). https://doi.org/10.1007/s00229-022-01376-0

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