Maximum principle for stable operators
Florian Grube, Thorben Hensiek
TL;DR
This paper establishes a weak maximum principle for nonlocal symmetric stable operators, including the fractional Laplacian, and investigates the regularity properties of functions under these operators.
Contribution
It introduces a maximum principle for a broad class of nonlocal operators and analyzes the regularity of functions associated with them.
Findings
Proves a weak maximum principle for symmetric stable operators.
Includes the fractional Laplacian as a special case.
Studies regularity properties of functions under these operators.
Abstract
We prove a weak maximum principle for nonlocal symmetric stable operators. This includes the fractional Laplacian. The main focus of this work is the regularity of the considered function.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems