| Issue |
ESAIM: COCV
Volume 13, Number 3, July-September 2007
|
|
|---|---|---|
| Page(s) | 484 - 502 | |
| DOI | https://doi.org/10.1051/cocv:2007021 | |
| Published online | 05 June 2007 | |
Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
1
Dipartimento di Matematica, Università ”Tor Vergata”, via della Ricerca Scientifica, 00133 Roma, Italy; cutri@mat.uniroma2.it
2
Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, 35131 Padova, Italy.
Received:
6
September
2005
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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