We consider a class of Lipschitz vector fields S: Omega --> R-n whose values lie in a suitable cone and we show that the trajectories of the system x' = S(x) admit a parametrization that is invertible and Lipschitz with its inverse. As a consequence, every nu in W-1,W-1 (Omega) admits a representative that is absolutely continuous on almost every trajectory of x' = S(x). If S is an arbritrary Lipschitz field the same property does hold locally at every x such that S(x) not equal 0. (C) 2003 Elsevier Science (USA). All rights reserved.
Absolutely continuous representatives on curves for Sobolev functions
MARICONDA, CARLO;TREU, GIULIA
2003
Abstract
We consider a class of Lipschitz vector fields S: Omega --> R-n whose values lie in a suitable cone and we show that the trajectories of the system x' = S(x) admit a parametrization that is invertible and Lipschitz with its inverse. As a consequence, every nu in W-1,W-1 (Omega) admits a representative that is absolutely continuous on almost every trajectory of x' = S(x). If S is an arbritrary Lipschitz field the same property does hold locally at every x such that S(x) not equal 0. (C) 2003 Elsevier Science (USA). All rights reserved.
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