Absolutely continuous functions of two varables in the sense of Carathéodory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00349672" target="_blank" >RIV/67985840:_____/10:00349672 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Absolutely continuous functions of two varables in the sense of Carathéodory

Popis výsledku v původním jazyce

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 certainintegral 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 rolein 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.

Název v anglickém jazyce

Absolutely continuous functions of two varables in the sense of Carathéodory

Popis výsledku anglicky

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 certainintegral 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 rolein 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F06%2F0254" target="_blank" >GA201/06/0254: Funkcionální diferenciální rovnice v Banachových prostorech</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Differential Equations

ISSN

1072-6691

e-ISSN

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Svazek periodika

2010

Číslo periodika v rámci svazku

154

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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