Abstract
AbstractGiven$$\alpha \in (0,1]$$α∈(0,1]and$$p\in [1,+\infty ]$$p∈[1,+∞], we define the space$${\mathcal {D}}{\mathcal {M}}^{\alpha ,p}({\mathbb {R}}^n)$$DMα,p(Rn)of$$L^p$$Lpvector fields whose$$\alpha $$α-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$$\alpha $$α-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.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Ministero dell’Istruzione, dell’Università e della Ricerca
HORIZON EUROPE European Research Council
Publisher
Springer Science and Business Media LLC
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