Harnack's Inequality and A Priori Estimates for Fractional Powers of Non-symmetric Differential Operators

Hugo Aimar; Gastón Beltritti; Ivana Gómez; Cristian Rios

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arXiv · 1610.03206

Harnack's Inequality and A Priori Estimates for Fractional Powers of Non-symmetric Differential Operators

Hugo Aimar·Gastón Beltritti·Ivana Gómez·Cristian Rios

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Abstract

We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order differential operators. These include weighted elliptic and subellitptic operators in divergence form (nonnecessarily self-adjoint), and nondivergence form operators with rough coefficients. We utilize the reflection extension technique introduced by Caffarelli and Silvestre.

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Hugo Aimar, Gastón Beltritti, Ivana Gómez, Cristian Rios. 2016-10-11. Harnack's Inequality and A Priori Estimates for Fractional Powers of Non-symmetric Differential Operators. https://arxiv.org/abs/1610.03206

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