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On Hamilton–Jacobi equations in bounded domains

Published online by Cambridge University Press:  14 November 2011

Hans Engler
Hans Engler
Affiliation:
Department of Mathematics, Georgetown University, Washington, D.C. 20057, U.S.A.
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Synopsis

Initial-boundary value problems for nonlinear first order partial differential equations ∂tu + H(x, t, u, Dxu) = 0 and corresponding boundary value problems H(x, u, Dxu) = 0 are studied in bounded sets, using Crandal's and Lions' notion of viscosity solutions. We give pointwise conditions on the boundary data that guarantee the existence of such solutions and estimate their moduli of continuity in terms of continuity properties of the data. The results are applied to properties of the value function for certain differential games.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 221 - 242
Copyright
Copyright © Royal Society of Edinburgh 1986

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