Caccioppoli sets
Bounded Variation Functions

Article REF: AF109 V1

Caccioppoli sets
Bounded Variation Functions

Author : Jean-Charles PINOLI

Publication date: May 10, 2025 | Lire en français

You do not have access to this resource.

Request your free trial access! Free trial

Already subscribed?Log in!

9. Caccioppoli sets

The notion of the Caccioppoli set was introduced in 1927-28 by the Italian mathematician R. Caccioppoli (1904-1959), and further developed in 1952-1958 by the Italian mathematician E. de Giorgi (1928-1996). This notion forms the basis of the modern theory of perimeters.

9.1 Definition

Definition (scope) (Caccioppoli, 1927). Let U be a nonempty open of $ℝ^{n}$ and B a Borellian subset of $ℝ^{n}$ . The perimeter of B in U, denoted Per(B,U), is the total variation of the indicator function 1 _...

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

Ongoing reading
Caccioppoli sets

Previous
page Numerical functions with particular bounded variations

Generalizations, extensions and restrictions

Article included in this offer

"Mathematics"

( 165 articles )

Complete knowledge base

Updated and enriched with articles validated by our scientific committees

Services

A set of exclusive tools to complement the resources

View offer details

Bibliography

(1) - ALBERTI (G.), MANTEGAZZA (C.) - A Note on the Theory of SBV Functions, - Bollettino Unione Matematica Italiana Sezione B, Vol. 7, n° 11, pp. 375-382 (1997).
(2) - AMBROSIO (L.) - Metric space valued functions with bounded variation, -...

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

Outline
Full outline