Lp estimates for the Caffarelli-Silvestre extension operators
Giorgio Metafune, Luigi Negro, Chiara Spina
TL;DR
This paper investigates Lp estimates for Caffarelli-Silvestre extension operators related to singular elliptic operators, providing new insights into their behavior in elliptic and parabolic problems on half-spaces.
Contribution
It introduces novel Lp estimate techniques for the extension operators associated with singular elliptic operators, advancing understanding of their analytical properties.
Findings
Established new Lp bounds for the operators
Analyzed elliptic and parabolic problem solutions
Provided applications to fractional Laplacian extensions
Abstract
We study elliptic and parabolic problems governed by the singular elliptic operators Delta_x+c\yD_y-b\y^2 on the half-space R^{N+1}_+.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems