Electron. J. Diff. Eqns., Vol. 2003(2003), No. 95, pp. 1-12.

Averaging for non-periodic fully nonlinear equations

Claudio Marchi

Abstract:
This paper studies the averaging problem for some fully nonlinear equations of degenerate parabolic type with a Hamiltonian not necessarily periodic in the fast variable. Our aim is to point out a sufficient condition on the Hamiltonian to pass to the limit in the starting equation. Also, we investigate when this condition is not completely fulfilled and discuss some examples concerning deterministic and stochastic optimal control problems.

Submitted July 22, 2003. Published September 17, 2003.
Math Subject Classifications: 34C29, 49L25, 49N70, 35B15.
Key Words: Averaging methods, viscosity solutions, differential games.

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Claudio Marchi
Dipartimento di Matematica Pura ed Applicata
Universita di Padova
via Belzoni 7, 35131 Padova, Italy} email: marchi@math.unipd.it

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