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Regularity for Hamilton-Jacobi equations via approximation

Published online by Cambridge University Press:  17 April 2009

Bum Il Hong
Bum Il Hong
Affiliation:
Department of MathematicsHoseo UniversityChoongnam 337–850Korea
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Abstract

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We prove new regularity results for solutions of first-order partial differential equations of Hamilton-Jacobi type posed as initial value problems on the real line. We show that certain spaces determined by quasinorms related to the solution's approximation properties in C(ℝ) by continuous, piecewise quadratic polynomial functions are invariant under the action of the differential equation. As a result, we show that solutions of Hamilton-Jacobi equations have enough regularity to be approximated well in C(ℝ) by moving-grid finite element methods. The preceding results depend on a new stability theorem for Hamilton-Jacobi equations in any number of spatial dimensions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 2 , April 1995 , pp. 195 - 213
Copyright
Copyright © Australian Mathematical Society 1995

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