document: Homogenization in L/sup infinity / Homogenization of deterministic control problems with L/sup infinity / running cost is studied by viscosity solutions techniques . It is proved that the value function of an L/sup infinity / problem in a medium with a periodic micro-structure converges uniformly on the compact sets to the value function of the homogenized problem as the period shrinks to 0 . Our main convergence result extends that of Ishii -LRB- Stochastic Analysis , control , optimization and applications , pp. 305-324 , Birkhauser Boston , Boston , MA , 1999 . -RRB- to the case of a discontinuous Hamiltonian . The cell problem is solved , but , as nonuniqueness occurs , the effective Hamiltonian must be selected in a careful way . The paper also provides a representation formula for the effective Hamiltonian and gives illustrations to calculus of variations , averaging and one-dimensional problems
doc_bio_tags: B O O O O B O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O B O O O
extractive_keyphrases: deterministic control homogenization value function averaging calculus of variations convergence cell problem
abstractive_keyphrases: l/sup infinity / running cost optimal control