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<p>We prove a local self-improving property for the gradient of very weak solutions to degenerate parabolic double-phase systems. The result is based on a reverse Hölder inequality with constants that are independent of the solution. Delicate methods are required to avoid a self-referential argument. In particular, we develop a new phase analysis method.</p>

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Very weak solutions to degenerate parabolic double-phase systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月4日

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  • Wontae Kim,
  • Lauri Särkiö

摘要

We prove a local self-improving property for the gradient of very weak solutions to degenerate parabolic double-phase systems. The result is based on a reverse Hölder inequality with constants that are independent of the solution. Delicate methods are required to avoid a self-referential argument. In particular, we develop a new phase analysis method.