Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula

被引：1
|
作者：
Comi, Giovanni E. [1 ]
Stefani, Giorgio [2 ]
机构：
[1] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, BO, Italy
[2] Scuola Int Super Avanzati SISSA, Via Bonomea 265, I-34136 Trieste, TS, Italy
来源：
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA | 2024年 / 17卷 / 02期
基金：
欧洲研究理事会;
关键词：
Fractional divergence-measure fields; Fractional calculus; Leibniz rule; Gauss-Green formula; Hausdorff measure; DISTRIBUTIONAL APPROACH; SOBOLEV SPACES; CAUCHY FLUXES; 1-LAPLACIAN; EXISTENCE; EQUATIONS;
D O I：
10.1007/s40574-023-00370-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：259 / 281
页数：23
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