English

Very weak solutions to degenerate parabolic double-phase systems

Analysis of PDEs 2025-12-18 v1

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.

Keywords

Cite

@article{arxiv.2512.15255,
  title  = {Very weak solutions to degenerate parabolic double-phase systems},
  author = {Wontae Kim and Lauri Särkiö},
  journal= {arXiv preprint arXiv:2512.15255},
  year   = {2025}
}