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Absolutely continuous functions of two variables in the sense of Carathéodory

SYSNO ASEP	0349672
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Absolutely continuous functions of two variables in the sense of Carathéodory
Author(s)	Šremr, Jiří (MU-W)_{RID, SAI, ORCID}
Source Title	Electronic Journal of Differential Equations. - : Texas State University - ISSN 1072-6691 Roč. 2010, č. 154 (2010), s. 1-11
Number of pages	11 s.
Language	eng - English
Country	US - United States
Keywords	absolutely continuous function ; Carathéodory sense ; integral representation ; derivative of double integral
Subject RIV	BA - General Mathematics
R&D Projects	GA201/06/0254 GA ČR - Czech Science Foundation (CSF)
CEZ	AV0Z10190503 - MU-W (2005-2011)
UT WOS	000208206000002
EID SCOPUS	78649698898
Annotation	In this note, the notion of absolute continuity of functions of two variables is discussed. We recall that the set of functions of two variables absolutely continuous in the sense of Caratheodory coincides with the class of functions admitting a certain integral representation. We show that absolutely continuous functions in the sense of Caratheodory can be equivalently characterized in terms of their properties with respect to each of variables. These equivalent characterizations play an important role in the investigation of boundary value problems for partial differential equation of hyperbolic type with discontinuous right-hand side. We present several statements which are rather important when analyzing strong solutions of such problems by using the methods of real analysis but, unfortunately, are not formulated and proven precisely in the existing literature, which mostly deals with weak solutions or the case where the right-hand side of the equation is continuous.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2011

Number of the records: 1