Volume 13, Number 3, July-September 2007
|Page(s)||484 - 502|
|Published online||05 June 2007|
Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
Dipartimento di Matematica, Università ”Tor Vergata”, via della Ricerca Scientifica, 00133 Roma, Italy; email@example.com
2 Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, 35131 Padova, Italy.
Revised: 24 March 2006
In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form in 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.
Mathematics Subject Classification: 70H20 / 49L25 / 35B05
Key words: Hamilton-Jacobi equations / sub-Riemannian metric / viscosity solution / comparison principle
© EDP Sciences, SMAI, 2007
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