 
Summary: Preprint di Matematica  n. 4 Maggio 2006
Dirichlet Problems for some
HamiltonJacobi Equations With
Inequality Constraints
JeanPierre Aubin
Alexandre M. Bayen
Patrick SaintPierre
SCUOLA NORMALE SUPERIORE
PISA
1
Dirichlet Problems for some HamiltonJacobi Equations With
Inequality Constraints
JeanPierre Aubin 1 2
, Alexandre M. Bayen3
and Patrick SaintPierre4
Abstract
We use viability techniques for solving Dirichlet problems with inequality constraints (obstacles) for
a class of HamiltonJacobi equations. The hypograph of the "solution" is defined as the "capture basin"
under an auxiliary control system of a target associated with the initial and boundary conditions, viable
in an environment associated with the inequality constraint. From the tangential condition characterizing
