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DTSTAMP;TZID=America/Vancouver:20221208T170000
DTSTART;TZID=America/Vancouver:20221208T170000
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UID:20221208T170000@prima2022.primamath.org
SUMMARY:Small $A_\infty$ results for Dahlberg-Kenig-Pipher operators in domains with low-dimensional, uniformly rectifiable boundaries
DESCRIPTION:In this talk, I will discuss joint work with M. Engelstein, L. Li, and S. Mayboroda, where we introduce the notion of Dahlberg-Kenig-Pipher operators in the context of domains $\Omega$ with low dimensional boundaries. We show that when the boundary of the domain is uniformly rectifiable with small constant, then elliptic measure $\omega$ associated to this domain is an $A_\infty(d\sigma)$ weight with small constant. As consequence, we show that for $C^1$ domains, $\log (d\omega/d\sigma) \in \mathrm{VMO}$. One of the main difficulties in this context is the lack of outer graphical approximations to $\Omega$, since the exterior of $\Omega$ can be empty.
STATUS:CONFIRMED
LOCATION:Parksville
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