On p-elliptic divergence form operators and holomorphic semigroups

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On p-elliptic divergence form operators and holomorphic semigroups

Egert, Moritz

Journal of evolution equations, 09/2020, Volume: 20, Issue: 3

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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–Dragičević and Dindoš–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. This has immediate consequences for the harmonic analysis of such operators, including H ∞ -calculi and Riesz transforms.

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Egert, Moritz

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