We consider the Cauchy problem u(t) + H(x, Du) = 0, (x, t) epsilon R-N x (0, infinity), u(x, 0) = u(0)(x), x epsilon R-N, where H is measurable in x, continuous, convex and positive homogeneous in p. We adapt the definition of viscosity solution to the measurable framework and we prove that the unique viscosity solution is given by a representation formula of Hopf-Lax type.
An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations
CAMILLI, FABIO
2004-01-01
Abstract
We consider the Cauchy problem u(t) + H(x, Du) = 0, (x, t) epsilon R-N x (0, infinity), u(x, 0) = u(0)(x), x epsilon R-N, where H is measurable in x, continuous, convex and positive homogeneous in p. We adapt the definition of viscosity solution to the measurable framework and we prove that the unique viscosity solution is given by a representation formula of Hopf-Lax type.File in questo prodotto:
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