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Oblique Derivative Problem for Parabolic Systems with Quadratic Nonlinearity in Gradient. Boundary Regularity Results

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We consider a class of quasilinear parabolic systems with strong (quadratic) nonlinearity in the gradient. Under a one-sided condition on the quadratic term, we study the boundary regularity of weak solutions to the oblique derivative problem. We describe conditions that guarantee the local Hölder continuity of weak (possibly unbounded) solutions.

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Authors and Affiliations

  1. St. Petersburg State University, 28, Universitetskii pr., Petrodvorets, St. Petersburg, 198504, 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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Dedicated to Nina Nikolaevna Uraltseva

Translated from Problemy Matematicheskogo Analiza 127, 2024, pp. 59-82.

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Arkhipova, A.A. Oblique Derivative Problem for Parabolic Systems with Quadratic Nonlinearity in Gradient. Boundary Regularity Results. J Math Sci 281, 537–565 (2024). https://doi.org/10.1007/s10958-024-07133-w

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