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arXiv · 2512.15255

Very weak solutions to degenerate parabolic double-phase systems

Wontae Kim·Lauri Särkiö
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Abstract

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 H\"older 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.

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Wontae Kim, Lauri Särkiö. 2025-12-17. Very weak solutions to degenerate parabolic double-phase systems. https://arxiv.org/abs/2512.15255

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