Work

Interior regularity of mixed local-nonlocal parabolic semilinear equations

Year: 2026

Type: preprint

Abstract: In this paper we prove the existence, uniqueness and regularity of classical solutions \break of a semilinear parabolic equation with a mixed local and nonlocal diffusion operator \break $\mathcal{L} = -(-Δ)^s + Δ$ and Dirichlet boundary conditions. Here, $(-Δ)^s$ is the integral fractional laplacian and $Δ$ is the classic local laplacian. We then study the interior regularity of said solutions and conclude that they are Hölder continuous in both space and time, and they are $C^{2,α}_{loc}$ in space for all positive times.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06537

Authors: Junquera, Sergio, Del Pezzo, Leandro M.

Institution: Universidad Complutense de Madrid

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agencia Nacional de Investigación e Innovación, Ministerio de Ciencia, Innovación y Universidades, European Regional Development Fund, Agencia Estatal de Investigación

Awards: G103507813, G1105844351, G1272900390, G1754140167, G1787261173, G2019505627, G410571670, G4212894969, G451917667, G491712853, G5539308778, G5635532810, G5967599077, G7805626310, G7863371703, G8497050386

OpenAlex ID: W7220735270

Cites: 21

Cited by: 1

Related to: 10