Počet záznamů: 1

Absolutely continuous functions of two variables in the sense of Carathéodory

  1. 1.
    0349672 - MU-W 2011 RIV US eng J - Článek v odborném periodiku
    Šremr, Jiří
    Absolutely continuous functions of two variables in the sense of Carathéodory.
    Electronic Journal of Differential Equations. Roč. 2010, č. 154 (2010), s. 1-11 ISSN 1072-6691
    Grant CEP: GA ČR(CZ) GA201/06/0254
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: absolutely continuous function * Carathéodory sense * integral representation * derivative of double integral
    Kód oboru RIV: BA - Obecná matematika

    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.
    Trvalý link: http://hdl.handle.net/11104/0189844
    Název souboruStaženoVelikostKomentářVerzePřístup
    Sremr.pdf2236.2 KBVydavatelský postprintpovolen