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 - <p style="text-align: justify;">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.</p>