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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a class of Lipschitz continuous functions of several variables
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by Tran Duc Van and Nguyen Duy Thai Son PDF
Proc. Amer. Math. Soc. 121 (1994), 865-870 Request permission

Abstract:

We establish an estimate via initial values for functions in a class of Lipschitz continuous functions of several variables. This estimate can be used to investigate the uniqueness of quasi-classical solutions of Cauchy problems for first-order nonlinear partial differential equations (PDEs). Particularly, we give an answer to an open problem posed by S. N. Kružkov.
References
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  • S. N. Kruzhkov, Theory of functions, and differential equations, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 5 (1991), 36–43, 96 (Russian, with Russian summary); English transl., Moscow Univ. Math. Bull. 46 (1991), no. 5, 30–35. MR 1294656
  • Tr\grcf{a}n Đú’c Vân and Nguyen Duy Thai Son, On the uniqueness of global classical solutions of the Cauchy problem for Hamilton-Jacobi equations, Acta Math. Vietnam. 17 (1992), no. 1, 161–167. MR 1190117
    • —, Uniqueness of global quasi-classical solutions of the Cauchy problem for the equation $\partial u/\partial t + {(\partial u/\partial x)^2} = 0$, Tạp chí Toán học 19 (1991), 65-71.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 865-870
  • MSC: Primary 26D10
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1227530-4
  • MathSciNet review: 1227530