We study the fractional Laplacian and the homogeneous Sobolev spaces on Rd, by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way, we also prove some properties of the fractional Laplacian.
Fractional Laplacian, homogeneous Sobolev spaces and their realizations / A. Monguzzi, M.M. Peloso, M. Salvatori. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2020). [Epub ahead of print]
Titolo: | Fractional Laplacian, homogeneous Sobolev spaces and their realizations |
Autori: | SALVATORI, MAURA ELISABETTA (Ultimo) |
Parole Chiave: | Homogeneous Sobolev spaces; Fractional Laplacian |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Progetto: | Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis |
Data di pubblicazione: | 2020 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10231-020-00966-7 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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