Gradient of the single layer potential and quantitative rectifiability for general Radon measures
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...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:250751 |
| Acceso en línea: | https://ddd.uab.cat/record/250751 https://dx.doi.org/urn:doi:10.1016/j.jfa.2021.109376 |
| Access Level: | acceso abierto |
| Palabra clave: | Singular integrals Rectifiability Elliptic measure Two-phase problems |
| Sumario: | 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. |
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