Work

Higher Hölder regularity for a subquadratic nonlocal parabolic equation

Year: 2024

Type: article

Abstract: In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation ∂ t u + ( − Δ p ) s u = 0 . Here, ( − Δ p ) s is the fractional p -Laplacian, 0 < s < 1 and 1 < p < 2 . We establish Hölder regularity with explicit Hölder exponents. We also include the inhomogeneous equation with a bounded inhomogeneity. In some cases, the obtained Hölder exponents are almost sharp. Our results complement the previous results for the superquadratic case when p ≥ 2 .

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2024.11.024

Authors: Prashanta Garain, Erik Lindgren, Alireza Tavakoli

Institutions: Indian Institute of Science Education and Research Berhampur, KTH Royal Institute of Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,050

Funders: Vetenskapsrådet, Indian Institute of Science Education and Research Pune, Indian Institute of Science Education and Research Mohali, Berhampur University