Gradient of the single layer potential and quantitative rectifiability for general Radon measures
Puliatti, Carmelo (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2022
Abstract:	We identify a set of sufficient local conditions under which a significant portion of a Radon measure μ on with compact support can be covered by an uniformly n-rectifiable set, at the level of a ball such that . This result involves a flatness condition, formulated in terms of the so-called -number of B, and the -boundedness, as well as a control on the mean oscillation on the ball, of the operator. Here is the fundamental solution for a uniformly elliptic operator in divergence form associated with an matrix with Hölder continuous coefficients. This generalizes a work by Girela-Sarrión and Tolsa for the n-Riesz transform. The motivation for our result stems from a two-phase problem for the elliptic harmonic measure.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-0395 Ministerio de Ciencia e Innovación MTM-2016-77635-P Ministerio de Economía y Competitividad MDM-2014-0445 Agencia Estatal de Investigación PID2020-114167GB-I00
Note:	Altres ajuts: acords transformatius de la UAB
Note:	Altres ajuts: Gobierno Vasco IT-1247-19
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Singular integrals ; Rectifiability ; Elliptic measure ; Two-phase problems
Published in:	Journal of functional analysiss, Vol. 282, Issue 6 (March 2022) , art. 109376, ISSN 1096-0783

DOI: 10.1016/j.jfa.2021.109376

77 p, 1.1 MB

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