A duality approach to the fractional Laplacian with measure data

Q: What type of study is this?

This is a Quantitative Study study.

Kenneth H. Karlsen; Francesco Petitta; Süleyman Ulusoy

doi:10.48550/arxiv.2508.06390

August 8, 2025Open Access

A duality approach to the fractional Laplacian with measure data

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Key Points

Existence and uniqueness of solutions are proven using a duality method.
The fractional Laplacian operator plays a crucial role in defining the problem.
Solutions are analyzed within the context of compactly supported Radon measures.
Vanishing conditions at infinity are essential for the problem's formulation.

Implication

This analysis demonstrates existence and uniqueness of solutions for nonlocal problems, highlighting measure data's role.

Abstract

We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like (-Δ)ˢ v = μ in\ RN, with vanishing conditions at infinity. Here $μ$ is a bounded Radon measure whose support is compactly contained in RN, N≥2, and -(Δ)ˢ is the fractional Laplace operator of order s∈ (1/2,1).

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Cite This Study

Karlsen et al. (2025) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a4eb https://doi.org/10.48550/arxiv.2508.06390

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A duality approach to the fractional Laplacian with measure data

Key Points

Implication

Abstract

Discussion

Cite This Study

A duality approach to the fractional Laplacian with measure data

Key Points

Implication

Abstract

Discussion

Cite This Study

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