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This is a Quantitative Study study.

October 16, 2025Journal of the London Mathematical Society

Riesz potential estimates for mixed local–nonlocal problems with measure data

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Pointwise bounds for the gradient were established, demonstrating the effectiveness of Riesz potential estimates.
The study focuses on mixed local–nonlocal problems involving bounded Borel measures in varying dimensions.
Truncated 1-Riesz potential forms the basis for deriving gradient regularity in the given mathematical framework.
Findings contribute to understanding the interplay between local and nonlocal modeling in mathematical analysis.

Implication

Analysis reveals bounds for gradient regularity in local–nonlocal problems, highlighting Riesz potential's role.

Abstract

We study gradient regularity for mixed local–nonlocal problems modeled upon for and , where is a bounded Borel measure and is the ambient dimension. We prove pointwise bounds for the gradient in terms of the truncated 1‐Riesz potential of .

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Cite This Study

Chlebicka et al. (2025) studied this question.

synapsesocial.com/papers/68f04935e559138a1a06e27d https://doi.org/10.1112/jlms.70310

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Implication

Analysis reveals bounds for gradient regularity in local–nonlocal problems, highlighting Riesz potential's role.

Riesz potential estimates for mixed local–nonlocal problems with measure data

Key Points

Implication

Abstract

Discussion

Cite This Study

Riesz potential estimates for mixed local–nonlocal problems with measure data

Key Points

Implication

Abstract

Discussion

Cite This Study

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