Work

Fine Boundary Continuity for Degenerate Double-Phase Diffusion

Year: 2025

Type: article

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

Source: Potential Analysis

DOI: 10.1007/s11118-025-10198-0

Authors: Simone Ciani, Eurica Henriques, Igor I. Skrypnik

Institutions: University of Bologna, University of Trás-os-Montes and Alto Douro, Centro de Matemática Pólo da Universidade de Trás-os-Montes e Alto Douro, University of Minho, National Academy of Sciences of Ukraine

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Simons Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", Università di Bologna, Fundação para a Ciência e a Tecnologia