Absolutely continuous functions of two varables in the sense of Carathéodory

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Absolutely continuous functions of two varables in the sense of Carathéodory
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F06%2F0254" target="_blank" >GA201/06/0254: Functional differential equations in Banach spaces</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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