TY - JOUR
T1 - The fractional variation and the precise representative of BVα,p functions
AU - Comi, Giovanni E.
AU - Spector, Daniel
AU - Stefani, Giorgio
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/4
Y1 - 2022/4
N2 - We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019). We provide a general analysis of the distributional space BVα,p(Rn) of Lp functions, with p∈ [1 , + ∞] , possessing finite fractional variation of order α∈ (0 , 1). Our two main results deal with the absolute continuity property of the fractional variation with respect to the Hausdorff measure and the existence of the precise representative of a BVα,p function.
AB - We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019). We provide a general analysis of the distributional space BVα,p(Rn) of Lp functions, with p∈ [1 , + ∞] , possessing finite fractional variation of order α∈ (0 , 1). Our two main results deal with the absolute continuity property of the fractional variation with respect to the Hausdorff measure and the existence of the precise representative of a BVα,p function.
KW - Fractional capacity
KW - Fractional divergence
KW - Fractional gradient
KW - Fractional variation
KW - Hausdorff measure
KW - Precise representative
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UR - https://www.mendeley.com/catalogue/54d31e6e-e748-3af7-8ac4-f9b9aa7eaa87/
U2 - 10.1007/s13540-022-00036-0
DO - 10.1007/s13540-022-00036-0
M3 - Article
AN - SCOPUS:85130388195
SN - 1311-0454
VL - 25
SP - 520
EP - 558
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
IS - 2
ER -