Numerical functions with bounded variations of several variables
Bounded Variation Functions

Article REF: AF109 V1

Numerical functions with bounded variations of several variables
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!

7. Numerical functions with bounded variations of several variables

This section considers functions of several real (or complex) variables with real (or complex) vector values.

7.1 Definitions

Definition (total variation). Let U be a non-empty open of $ℝ^{n}$ . The total variation of a function belonging to $L^{1} (U, ℝ)$ is defined as follows:

T V (f, U) := sup {

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
Numerical functions with bounded variations of several variables

Previous
page Numerical functions with bounded variations of one variable

Numerical functions with particular bounded variations

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