Estimates of the Green function for the fractional Laplacian perturbed by gradient
Krzysztof Bogdan, Tomasz Jakubowski
TL;DR
This paper compares the Green functions of the fractional Laplacian and its gradient-perturbed version for smooth bounded domains, under certain conditions on the drift function.
Contribution
It establishes the comparability of Green functions for the fractional Laplacian and its gradient perturbations in bounded smooth domains with drift functions in a Kato class.
Findings
Green functions are comparable under specified conditions.
Results apply to differential orders greater than one.
Provides a framework for analyzing perturbed fractional Laplacians.
Abstract
The Green function of the fractional Laplacian of the differential order bigger than one and the Green function of its gradient perturbations are comparable for bounded smooth multidimensional open sets if the drift function is in an appropriate Kato class.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems