We prove necessary conditions for a solution u to the problem of minimizing fΩ[f (∥∇v (x)∥) + g(x,v(x))]dx in the form of a Pontryagin maximum principle, for f convex and satisfying a growth assumption, but without assuming differentiability. © 2009 Society for Industrial and Applied Mathematics.
Cellina, A., Mazzola, M. (2009). Necessary conditions for solutions to variational problems. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 48, 2977-2983.
Necessary conditions for solutions to variational problems
CELLINA, ARRIGO;
2009
Abstract
We prove necessary conditions for a solution u to the problem of minimizing fΩ[f (∥∇v (x)∥) + g(x,v(x))]dx in the form of a Pontryagin maximum principle, for f convex and satisfying a growth assumption, but without assuming differentiability. © 2009 Society for Industrial and Applied Mathematics.
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