Gronwall's inequality in independent variables

Author:
Eutiquio C. Young

Journal:
Proc. Amer. Math. Soc. **41** (1973), 241-244

MSC:
Primary 35B45

DOI:
https://doi.org/10.1090/S0002-9939-1973-0320493-1

MathSciNet review:
0320493

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Abstract: The paper presents an extension of Gronwall's inequality to 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:
https://doi.org/10.1090/S0002-9939-1973-0320493-1

Keywords:
Gronwall's inequality,
hyperbolic differential equation,
characteristic initial value problem,
Riemann function,
integral equation

Article copyright:
© Copyright 1973
American Mathematical Society