# Mathematical Sciences Research Institute

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# Seminar

Harmonic Analysis Seminar: On boundary value problems for parabolic equations with time-dependent measurable coefficients April 24, 2017 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: Harmonic Analysis MSRI: Simons Auditorium
Speaker(s) Pascal Auscher (Université de Paris XI)
Description No Description
Video
We will explain the proof of a Carleson measure estimate on solutions of parabolic equations with real measurable time-dependent coefficients that implies that the parabolic measure is an $A_\infty$ weight.
This corresponds to the parabolic analog of a recent result by Hofmann, Kenig, Mayboroda and Pipher for elliptic equations. Our proof even simplifies theirs. As is well known, the $A_\infty$ property implies that   $L^p$ Dirichlet problem is well-posed. An important ingredient of the proof is a Kato square root property for parabolic operators on the boundary, which can be seen as a consequence of certain square function estimates applicable to Neumann and regularity problems.  All this is  joint work with Moritz Egert and Kaj Nyström.