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Generalized convexity of power functions

Oliver Dragicevic
University of Ljubljana
Luigi Stasi Seminar Room, ICTP
Thursday, December 5, 2019 - 16:00

We study elliptic partial differential operators in divergence form on open sets in $\mathbb{R}^n$ and associated with complex uniformly strictly accretive matrices. We present several results for such operators, the central being the so-called bilinear embedding theorem. The proof of this theorem is a combination of heat flows and Bellman functions, and leads to a new concept of convexity of power functions $|z|^p$ for complex $z$ and associated with accretive matrices. This concept turns out to be a generalization of the classical ellipticity condition and seems to be well suited for the study of elliptic PDE on $L^p$ spaces.

The talk is based on collaboration with Andrea Carbonaro (U. Genova)

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