On p-elliptic divergence form operators and holomorphic semigroups

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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References in corpus (3)

• Lp-estimates for the square root of elliptic systems with mixed boundary conditions
• On the $L^p$-theory of $C_0$-semigroups associated with second-order elliptic operators with complex singular coefficients
• On the ${\mathrm{L}}^p$-theory for second-order elliptic operators in divergence form with complex coefficients

Cited by in corpus (5)

• Euclidean structures and operator theory in Banach spaces
• Trilinear embedding for divergence-form operators with complex coefficients
• A survey of functional and $L^p$ dissipativity theory
• Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_p$
• Criterion for the functional dissipativity of the Lamé operator