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arXiv · 2403.06550

Fine boundary continuity for degenerate double-phase diffusion

Simone Ciani·Eurica Henriques·Igor Skrypnik
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Abstract

We study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown in terms of either its $p$ or $q$ capacity, depending on whether the phase vanishes at the boundary or not. Eventually we obtain a fine boundary estimate that, when considering uniform geometric conditions as density or fatness, leads us to the boundary H\"older continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity.

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Simone Ciani, Eurica Henriques, Igor Skrypnik. 2024-03-11. Fine boundary continuity for degenerate double-phase diffusion. https://arxiv.org/abs/2403.06550

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