Work

Nonlocal equations with degenerate weights

Year: 2024

Type: preprint

Abstract: We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincaré inequalities. When the order of fractional differentiability goes to $0$ or $1$, we recover the weighted Lebesgue and Sobolev spaces with Muckenhoupt weights, respectively. Moreover, we prove interior Hölder continuity and Harnack inequalities for solutions to the corresponding weighted nonlocal integro-differential equations. This naturally extends a classical result by Fabes, Kenig, and Serapioni to the nonlinear, nonlocal setting.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2409.11829

Authors: Behn, Linus, Diening, Lars, Ok, Jihoon, Rolfes, Julian

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, Deutsche Forschungsgemeinschaft, National Research Foundation of Korea

Awards: G1288578048, G2442903552, G2824978191, GRK 2235: Das Reguläre im Irregulären: Analysis von singulären und zufälligen Systemen, G467907816, G8201362140, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen

OpenAlex ID: W4403742425

Cites:

Cited by:

Related to: 10