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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 248 - Real Analysis Seminar
Dr. Ziming Shi
UC Irvine
Sobolev and Hölder estimate for the $\overline \partial$ equation on pseudoconvex domains of finite type in $\mathbb C^2$
Abstract:
We prove a homotopy formula which yields almost sharp estimates in all (positive-indexed) Sobolev and Hölder-Zygmund spaces for the $\overline \partial$ equation on finite type domains in $\mathbb C^2$, extending the earlier results of Fefferman-Kohn (1988), Range (1990), and Chang-Nagel-Stein (1992). The main novelty of our proof is the construction of holomorphic support functions that admit precise estimates when the parameter variable lies in a thin shell outside the domain, which generalizes Range's method.
Hosts: John N. Treuer and Ming Xiao
March 6, 2025
4:00 PM
APM 7218
Research Areas
Complex Variables Functional Analysis / Operator Theory****************************
