Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Santiesteban, Daniel Alfonso, Blaya, Ricardo Abreu, Alpay, Daniel
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866912809730703360
author Santiesteban, Daniel Alfonso
Blaya, Ricardo Abreu
Alpay, Daniel
author_facet Santiesteban, Daniel Alfonso
Blaya, Ricardo Abreu
Alpay, Daniel
contents The Clifford algebra language allows us to rewrite the Lamé-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is whether or not a higher order Lipschitz function on the boundary $Γ$ of a Jordan domain $Ω\subset\mathbb{R}^m$ can be decomposed into a sum of the two boundary values of a solution of the Lamé-Navier system with jump across $Γ$. Our main tool are the Hardy projections related to a singular integral operator arising in the context of Clifford analysis, which turns out to be an involution operator on the first order Lipschitz classes.
format Preprint
id arxiv_https___arxiv_org_abs_2601_04528
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions
Santiesteban, Daniel Alfonso
Blaya, Ricardo Abreu
Alpay, Daniel
Analysis of PDEs
Mathematical Physics
30G35
The Clifford algebra language allows us to rewrite the Lamé-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is whether or not a higher order Lipschitz function on the boundary $Γ$ of a Jordan domain $Ω\subset\mathbb{R}^m$ can be decomposed into a sum of the two boundary values of a solution of the Lamé-Navier system with jump across $Γ$. Our main tool are the Hardy projections related to a singular integral operator arising in the context of Clifford analysis, which turns out to be an involution operator on the first order Lipschitz classes.
title Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions
topic Analysis of PDEs
Mathematical Physics
30G35
url https://arxiv.org/abs/2601.04528