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Summary: Preprint di Matematica - n. 4 Maggio 2006
Dirichlet Problems for some
Hamilton-Jacobi Equations With
Inequality Constraints
Jean-Pierre Aubin
Alexandre M. Bayen
Patrick Saint-Pierre
SCUOLA NORMALE SUPERIORE
PISA
1
Dirichlet Problems for some Hamilton-Jacobi Equations With
Inequality Constraints
Jean-Pierre Aubin 1 2
, Alexandre M. Bayen3
and Patrick Saint-Pierre4
Abstract
We use viability techniques for solving Dirichlet problems with inequality constraints (obstacles) for
a class of Hamilton-Jacobi 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
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