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Volume 4, Issue 3
Variational Functionals for the Characterization of BV and Sobolev Spaces

Serena Guarino Lo Bianco & Roberta Schiattarella

DOI: 10.4208/cmaa.2025-0012

Commun. Math. Anal. Appl., 4 (2025), pp. 419-437.

Published online: 2025-09

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  • Abstract

This paper examines the characterization of bounded variation (BV) and Sobolev functions by using some non-local functionals. We analyze their pointwise convergence and establish a connection with the Sobolev norm and the total variation measure. By investigating a wider class of non local functionals, we provide a deeper understanding of how these approximations capture the local properties of BV and Sobolev spaces, thereby reinforcing their applicability in the Euclidean setting.

  • Keywords

BMO-type seminorms, Sobolev spaces, functions of bounded variation.

  • AMS Subject Headings

46E35, 26A45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-4-419, author = {Bianco , Serena Guarino Lo and Schiattarella , Roberta}, title = {Variational Functionals for the Characterization of BV and Sobolev Spaces}, journal = {Communications in Mathematical Analysis and Applications}, year = {2025}, volume = {4}, number = {3}, pages = {419--437}, abstract = {

This paper examines the characterization of bounded variation (BV) and Sobolev functions by using some non-local functionals. We analyze their pointwise convergence and establish a connection with the Sobolev norm and the total variation measure. By investigating a wider class of non local functionals, we provide a deeper understanding of how these approximations capture the local properties of BV and Sobolev spaces, thereby reinforcing their applicability in the Euclidean setting.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2025-0012}, url = {http://global-sci.org/intro/article_detail/cmaa/24336.html} }
TY - JOUR T1 - Variational Functionals for the Characterization of BV and Sobolev Spaces AU - Bianco , Serena Guarino Lo AU - Schiattarella , Roberta JO - Communications in Mathematical Analysis and Applications VL - 3 SP - 419 EP - 437 PY - 2025 DA - 2025/09 SN - 4 DO - http://doi.org/10.4208/cmaa.2025-0012 UR - https://global-sci.org/intro/article_detail/cmaa/24336.html KW - BMO-type seminorms, Sobolev spaces, functions of bounded variation. AB -

This paper examines the characterization of bounded variation (BV) and Sobolev functions by using some non-local functionals. We analyze their pointwise convergence and establish a connection with the Sobolev norm and the total variation measure. By investigating a wider class of non local functionals, we provide a deeper understanding of how these approximations capture the local properties of BV and Sobolev spaces, thereby reinforcing their applicability in the Euclidean setting.

Bianco , Serena Guarino Lo and Schiattarella , Roberta. (2025). Variational Functionals for the Characterization of BV and Sobolev Spaces. Communications in Mathematical Analysis and Applications. 4 (3). 419-437. doi:10.4208/cmaa.2025-0012
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