[HTML][HTML] Random Lax–Oleinik semigroups for Hamilton–Jacobi systems
A Davini, A Siconolfi, M Zavidovique - Journal de Mathématiques Pures et …, 2018 - Elsevier
Following the random approach of [1], we define a Lax–Oleinik formula adapted to evolutive
weakly coupled systems of Hamilton–Jacobi equations. It is reminiscent of the
corresponding scalar formula, with the relevant difference that it has a stochastic character
since it involves, loosely speaking, random switchings between the various associated
Lagrangians. We prove that the related value functions are viscosity solutions to the system,
and establish existence of minimal random curves under fairly general hypotheses. Adding …
weakly coupled systems of Hamilton–Jacobi equations. It is reminiscent of the
corresponding scalar formula, with the relevant difference that it has a stochastic character
since it involves, loosely speaking, random switchings between the various associated
Lagrangians. We prove that the related value functions are viscosity solutions to the system,
and establish existence of minimal random curves under fairly general hypotheses. Adding …
Random Lax–Oleinik semigroups for Hamilton–Jacobi systems
A Siconolfi, A Davini, M Zavidovique - … PURES ET APPLIQUÉES, 2017 - iris.uniroma1.it
Following the random approach of, we define a Lax-Oleinik formula adapted to evolutive
weakly coupled systems of Hamilton-Jacobi equations. It is reminiscent of the corresponding
scalar formula, with the relevant difference that it has a stochastic character since it involves,
loosely speaking, random switchings between the various associated Lagrangians. We
prove that the related value functions are viscosity solutions to the system, and establish
existence of minimal random curves under fairly general hypotheses. Adding Tonelli like …
weakly coupled systems of Hamilton-Jacobi equations. It is reminiscent of the corresponding
scalar formula, with the relevant difference that it has a stochastic character since it involves,
loosely speaking, random switchings between the various associated Lagrangians. We
prove that the related value functions are viscosity solutions to the system, and establish
existence of minimal random curves under fairly general hypotheses. Adding Tonelli like …
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