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}
}