Higher Hölder regularity for a subquadratic nonlocal parabolic equation
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 .
Authors
- Prashanta Garain (ORCID: https://orcid.org/0000-0001-6285-9329)
- Erik Lindgren (ORCID: https://orcid.org/0000-0003-4309-9242)
- Alireza Tavakoli (ORCID: https://orcid.org/0000-0003-0490-5205)
Institutions
- Indian Institute of Science Education and Research Berhampur (IN)
- KTH Royal Institute of Technology (SE)
Publication Details
- Journal
- Journal of Differential Equations
- Published
- 2024-11-29
- DOI
- https://doi.org/10.1016/j.jde.2024.11.024
- Citations
- 2
- Primary Topic
- Differential Equations and Boundary Problems
- Type
- article
- Field-Weighted Citation Impact
- 1.95
Funders
- Vetenskapsrådet
- Indian Institute of Science Education and Research Pune
- Berhampur University