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March 15, 2026Journal of the London Mathematical Society3 citationsOpen Access

Schauder estimates for parabolic p‐Laplace systems

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VBVerena BögeleinFDFrank DuzaarUniversity of SalzburgUGUgo Gianazza

Key Points

  • This research aims to establish the local Hölder regularity of the spatial gradient in bounded weak solutions for parabolic p-Laplace systems.
  • Analyzed the nonlinear parabolic system with bounded coefficients
  • Investigated the conditions for Hölder continuity in spatial variables
  • Applied the findings to a doubly nonlinear parabolic equation in fast diffusion regime.
  • Demonstrated local Hölder regularity of spatial gradients in bounded weak solutions
  • Proved Hölder estimates for gradients in supercritical diffusion scenarios.

Abstract

Abstract We establish the local Hölder regularity of the spatial gradient of bounded weak solutions to the nonlinear system of parabolic type where , , and the coefficient is bounded below by a positive constant and is Hölder continuous in the space variable . As an application, we prove Hölder estimates for the gradient of weak solutions to a doubly nonlinear parabolic equation in the supercritical fast diffusion regime.

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Cite This Study

Bögelein et al. (2026) studied this question.

synapsesocial.com/papers/69b64d5cb42794e3e660e289https://doi.org/10.1112/jlms.70463
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