Ciani: Fine boundary continuity for degenerate double-phase diffusion

Date: 2024-05-23

Time: 16:30 - 17:00

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Simone Ciani, University of Bologna


We present a study on 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.

This is a joint work in collaboration with Eurica Henriques and Ihor Skrypnik.