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arXiv · 1812.09154

On p-elliptic divergence form operators and holomorphic semigroups

Moritz Egert
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Abstract

Second order divergence form operators are studied on an open set with various boundary conditions. It is shown that the p-ellipticity condition of Carbonaro-Dragicevic and Dindos-Pipher implies extrapolation to a holomorphic semigroup on Lebesgue spaces in a p-dependent range of exponents that extends the maximal range for general strictly elliptic coefficients. Results have immediate consequences for the harmonic analysis of such operators, including Hoo-calculi and Riesz transforms.

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Moritz Egert. 2018-12-21. On p-elliptic divergence form operators and holomorphic semigroups. https://doi.org/10.1007/s00028-019-00537-1

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