Very weak solutions to degenerate parabolic double-phase systems

2025/12/17 by Kim, Wontae, Särkiö, Lauri
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.15255

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 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.

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