On a Class of Lipschitz Continuous Functions of Several Variables

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jul 1994Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 121, page 865 (issn: 0002-9939,

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Authors: Tran Duc Van; Nguyen Duy Thai Son;

doi: 10.2307/2160287 , 10.1090/s0002-9939-1994-1227530-4

On a Class of Lipschitz Continuous Functions of Several Variables

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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.

Keywords

Other analytical inequalities, Cauchy problems for first-order nonlinear partial differential equations, Initial value problems for nonlinear first-order PDEs

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