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Quasilinear Elliptic and Parabolic Systems with Nondiagonal Principal Matrices and Strong Nonlinearities in the Gradient. Solvability and Regularity Problems

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Abstract

We consider nondiagonal elliptic and parabolic systems of equations with strongly nonlinear terms in the gradient. We review and comment known solvability and regularity results and describe the our last results in this field.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. A. Arkhipova

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  1. A. A. Arkhipova
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Correspondence to A. A. Arkhipova.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 69, No. 1, Differential and Functional Differential Equations, 2023.

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Arkhipova, A.A. Quasilinear Elliptic and Parabolic Systems with Nondiagonal Principal Matrices and Strong Nonlinearities in the Gradient. Solvability and Regularity Problems. J Math Sci 283, 183–194 (2024). https://doi.org/10.1007/s10958-024-07248-0

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