Work

The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat domains

Year: 2025

Type: article

Abstract: In this paper we show that, given a planar Reifenberg flat domain with small constant and a divergence form operator associated to a real (not necessarily symmetric) uniformly elliptic matrix with Lipschitz coefficients, the Hausdorff dimension of its elliptic measure is at most 1. More precisely, we prove that there exists a subset of the boundary with full elliptic measure and with $$\sigma $$ σ -finite one-dimensional Hausdorff measure. For Reifenberg flat domains, this result extends a previous work of Thomas H. Wolff for the harmonic measure.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-025-01067-5

Authors: Ignasi Guillén-Mola, Martí Prats, Xavier Tolsa

Institutions: Universitat Autònoma de Barcelona, Institució Catalana de Recerca i Estudis Avançats, Centre de Recerca Matemàtica

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290