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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Gronwall's inequality in $ n$ independent variables


Author: Eutiquio C. Young
Journal: Proc. Amer. Math. Soc. 41 (1973), 241-244
MSC: Primary 35B45
MathSciNet review: 0320493
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Abstract: The paper presents an extension of Gronwall's inequality to $ n$ independent variables. The inequality is established by solving a characteristic initial value problem by the Riemann method. Thus a Riemann function associated with a hyperbolic partial differential equation appears in the inequality. By using a representation of the Riemann function, the result is shown to coincide with an earlier result obtained by Walter using an entirely different approach.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0320493-1
PII: S 0002-9939(1973)0320493-1
Keywords: Gronwall's inequality, hyperbolic differential equation, characteristic initial value problem, Riemann function, integral equation
Article copyright: © Copyright 1973 American Mathematical Society