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.

引用

页码：259 / 281

页数：23

共 29 条

[21] An extension of the pairing theory between divergence-measure fields and BV functions
Crasta, Graziano
De Cicco, Virginia
JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 276 (08) : 2605 - 2635
[22] Representation formulas for pairings between divergence-measure fields and BV functions
Comi, Giovanni E.
Crasta, Graziano
De Cicco, Virginia
Malusa, Annalisa
JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (01)
[23] Measures in the dual of RV: perimeter bounds and relations with divergence-measure fields
Comi, Giovanni E.
Leonardi, Gian Paolo
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2025, 251
[24] On BV functions and essentially bounded divergence-measure fields in metric spaces
Buffa, Vito
Comi, Giovanni E.
Miranda, Michele Jr Jr
REVISTA MATEMATICA IBEROAMERICANA, 2022, 38 (03) : 883 - 946
[25] PARSEVALS FORMULA AS A SPECIAL CASE OF LEIBNIZ RULE FOR FRACTIONAL DERIVATIVES
OSLER, TJ
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 18 (01): : 145 - &
[26] Divergence-Lq and divergence-measure tensor fields and gradient flows for linear growth functionals of maps into the unit sphere
Xiaobing Feng
Calculus of Variations and Partial Differential Equations, 2010, 37 : 111 - 139
[27] Divergence-Lq and divergence-measure tensor fields and gradient flows for linear growth functionals of maps into the unit sphere
Feng, Xiaobing
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (1-2) : 111 - 139
[28] Gauss-Green Theorem for Weakly Differentiable Vector Fields, Sets of Finite Perimeter, and Balance Laws
Chen, Gui-Qiang
Torres, Monica
Ziemer, William P.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (02) : 242 - 304
[29] The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces
Gorny, Wojciech
Mazon, J. M.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2024, 26 (06)

← 1 2 3 →