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 - Funding Information:
The first author is a member of INdAM–GNAMPA and is partially supported by the PRIN 2017 Project Variational methods for stationary and evolution problems with singularities and interfaces (n. prot. 2017BTM7SN). The second author is supported by the Taiwan Ministry of Science and Technology under research grant number 110-2115-M-003-020-MY3 and the Taiwan Ministry of Education under the Yushan Fellow Program. Part of this work was undertaken while the second author was visiting the National Center for Theoretical Sciences in Taiwan. He would like to thank the NCTS for its support and warm hospitality during the visit. The third author is a member of INdAM–GNAMPA and is partially supported by the ERC Starting Grant 676675 FLIRT – Fluid Flows and Irregular Transport and by the INdAM–GNAMPA Project 2020 Problemi isoperimetrici con anisotropie (n. prot. U-UFMBAZ-2020-000798 15-04-2020).
Funding Information:
The first author is a member of INdAM–GNAMPA and is partially supported by the PRIN 2017 Project Variational methods for stationary and evolution problems with singularities and interfaces (n. prot. 2017BTM7SN). The second author is supported by the Taiwan Ministry of Science and Technology under research grant number 110-2115-M-003-020-MY3 and the Taiwan Ministry of Education under the Yushan Fellow Program. Part of this work was undertaken while the second author was visiting the National Center for Theoretical Sciences in Taiwan. He would like to thank the NCTS for its support and warm hospitality during the visit. The third author is a member of INdAM–GNAMPA and is partially supported by the ERC Starting Grant 676675 FLIRT – Fluid Flows and Irregular Transport and by the INdAM–GNAMPA Project 2020 Problemi isoperimetrici con anisotropie (n. prot. U-UFMBAZ-2020-000798 15-04-2020).
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
VL - 25
SP - 520
EP - 558
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
SN - 1311-0454
IS - 2
ER -