We study Hopf-Lax formulas and invariant measures in the context of idempotent analysis. We show that idempotent analogue of the semigroup associated with the Ornstein-Uhlenbeck operator has a particularly simple invariant measure, and how this observation can be used in the analysis of the Hopf-Lax semigroup and viscosity solutions of the Hamilton-Jacobi equations. Further we introduce adjoint operators with respect to the Hopf- Lax semigroup and study their properties in the special case when the initial data of the Cauchy problem are linear functions.
Idempotent Aspects of Hopf-Lax Type Formulas / Avantaggiati, A; Loreti, Paola. - 495:(2009), pp. 103-114. (Intervento presentato al convegno International workshop TROPICAL-07 Tropical and Idempotent Mathematics tenutosi a Moscow; Russia nel August 25-30, 2007).
Idempotent Aspects of Hopf-Lax Type Formulas
LORETI, Paola
2009
Abstract
We study Hopf-Lax formulas and invariant measures in the context of idempotent analysis. We show that idempotent analogue of the semigroup associated with the Ornstein-Uhlenbeck operator has a particularly simple invariant measure, and how this observation can be used in the analysis of the Hopf-Lax semigroup and viscosity solutions of the Hamilton-Jacobi equations. Further we introduce adjoint operators with respect to the Hopf- Lax semigroup and study their properties in the special case when the initial data of the Cauchy problem are linear functions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
