Given a E (0, 1] and p E [1, +co], we define the space DMa,p(R-n) of L-p vector fields whose a-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the a-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples.
Comi G.E., Stefani G. (2023). Fractional divergence-measure fields, Leibniz rule and Gauss–Green formula. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, First published online, 1-23 [10.1007/s40574-023-00370-y].
Fractional divergence-measure fields, Leibniz rule and Gauss–Green formula
Comi G. E.;
2023
Abstract
Given a E (0, 1] and p E [1, +co], we define the space DMa,p(R-n) of L-p vector fields whose a-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the a-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples.| File | Dimensione | Formato | |
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