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<p>We consider a class of nonlinear parabolic systems with strong ((quadratic) nonlinearity in the gradient. Under a one-sided condition on the quadratic term, we establish the partial Hölder continuity of weak ((possibly, unbounded) solutions and their gradients. Bibliography: 23 titles.</p>

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REGULARITY PROBLEM FOR PARABOLIC SYSTEMS WITH QUADRATIC NONLINEARITY IN THE GRADIENT

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  • 发表日期：

    2025年7月23日

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  • A. A. Arkhipova

摘要

We consider a class of nonlinear parabolic systems with strong ((quadratic) nonlinearity in the gradient. Under a one-sided condition on the quadratic term, we establish the partial Hölder continuity of weak ((possibly, unbounded) solutions and their gradients. Bibliography: 23 titles.