Data di Pubblicazione:
2023
Citazione:
Some notes on functions of least Ws,1 -fractional seminorm / C. Bucur. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - 14:1(2023 Jul 06), pp. 38-57. [10.6092/issn.2240-2829/17270]
Abstract:
In this survey we discuss some existence and asymptotic results, originally obtained in [4,3], for functions of least Ws,1-fractional seminorm. We present the connection between these functions and nonlocal minimal surfaces, leveraging this relation to build a function of least fractional seminorm. We further prove that a function of least fractional seminorm is the limit for p → 1 of the sequence of minimizers of the Ws,p-energy. Additionally, we consider the fractional 1-Laplace operator and study the equivalence between weak solutions and functions of least fractional seminorm.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Fractional 1-Laplacian; nonlocal operators; nonlocal minimal surfaces;
Elenco autori:
C. Bucur
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