Functions of bounded variation and the AM-modulus in R-n

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390783" target="_blank" >RIV/00216208:11320/18:10390783 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.na.2018.05.015" target="_blank" >https://doi.org/10.1016/j.na.2018.05.015</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.na.2018.05.015" target="_blank" >10.1016/j.na.2018.05.015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Functions of bounded variation and the AM-modulus in R-n

Popis výsledku v původním jazyce

Moduli of path families are widely used to study Sobolev functions. Similarly, the recently introduced approximation (AM-) modulus is helpful in the theory of functions of bounded variation (BV) in R-n (Martio, 2016). We continue this direction of research. Let Gamma(E) be the family of all paths which meet E subset of R-n. We introduce the outer measure E bar right arrow AM(Gamma(E)) and compare it with other (n - 1)-dimensional measures. In particular, we show that AM(Gamma(E)) = 2H(n-1)(Gamma(E)) whenever E lies on a countably (n - 1)-rectifiable set. Further, we study functions which have bounded variation on AM-a.e. path and we relate these functions to the classical BV functions which have only bounded essential variation on AM-a.e. path. We also characterize sets E of finite perimeter in terms of the AM-modulus of two path families naturally associated with E. (C) 2018 Elsevier Ltd. All rights reserved.

Název v anglickém jazyce

Functions of bounded variation and the AM-modulus in R-n

Popis výsledku anglicky

Moduli of path families are widely used to study Sobolev functions. Similarly, the recently introduced approximation (AM-) modulus is helpful in the theory of functions of bounded variation (BV) in R-n (Martio, 2016). We continue this direction of research. Let Gamma(E) be the family of all paths which meet E subset of R-n. We introduce the outer measure E bar right arrow AM(Gamma(E)) and compare it with other (n - 1)-dimensional measures. In particular, we show that AM(Gamma(E)) = 2H(n-1)(Gamma(E)) whenever E lies on a countably (n - 1)-rectifiable set. Further, we study functions which have bounded variation on AM-a.e. path and we relate these functions to the classical BV functions which have only bounded essential variation on AM-a.e. path. We also characterize sets E of finite perimeter in terms of the AM-modulus of two path families naturally associated with E. (C) 2018 Elsevier Ltd. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-07996S" target="_blank" >GA18-07996S: Geometrická a harmonická analýza</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Nonlinear Analysis, Theory, Methods and Applications

ISSN

0362-546X

e-ISSN

—

Svazek periodika

2018

Číslo periodika v rámci svazku

177

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

19

Strana od-do

553-571

Kód UT WoS článku

000449073400012

EID výsledku v databázi Scopus

2-s2.0-85049353781