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arXiv · 2512.11294

Gradient higher integrability of bounded solutions to parabolic double-phase systems

Iwona Chlebicka·Prashanta Garain·Wontae Kim
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Abstract

We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\,, \] where a nonnegative weight $a$ is $\alpha$-H\"older continuous in space and $\tfrac \alpha 2$-H\"older continuous in time, have locally higher integrable gradients for the sharp range of exponents $p<q\le p+\alpha$.

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Iwona Chlebicka, Prashanta Garain, Wontae Kim. 2025-12-12. Gradient higher integrability of bounded solutions to parabolic double-phase systems. https://arxiv.org/abs/2512.11294

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