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<p>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 <i>p</i> or <i>q</i> 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 Hölder continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity.</p>

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Fine Boundary Continuity for Degenerate Double-Phase Diffusion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月20日

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  • Simone Ciani,
  • Eurica Henriques,
  • Igor I. Skrypnik

摘要

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 Hölder continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity.