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Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations

Published online by Cambridge University Press:  05 June 2007

Alessandra Cutrì  and
Francesca Da Lio
Alessandra Cutrì
Affiliation:
Dipartimento di Matematica, Università ”Tor Vergata”, via della Ricerca Scientifica, 00133 Roma, Italy; cutri@mat.uniroma2.it
Francesca Da Lio
Affiliation:
Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, 35131 Padova, Italy.
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Abstract

In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_t+H(x,Du) = 0$ in ${\rm I}\!{\rm R}^n\times(0,T)$ where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.

Keywords

Hamilton-Jacobi equationssub-Riemannian metricviscosity solutioncomparison principle
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 3 , July 2007 , pp. 484 - 502
Copyright
© EDP Sciences, SMAI, 2007

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