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Backward Ornstein-Uhlenbeck Transition Operators and Mild Solutions of Non-Autonomous Hamilton-Jacobi Equations in Banach Spaces

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Date
2014-10-09
Author
Serrano, RafaelAutoridad Universidad de Rosario
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Citation
URI

http://repository.urosario.edu.co/handle/10336/14405

Summary

In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property of Ornstein-Uhlenbeck transition evolution operators for stochastic Cauchy problems in Banach spaces with time-dependent coefficients.
Subject
Ornstein-Uhlenbeck Processes ; Infinite-Dimensional Hamilton-Jacobi Equations ; Mild Solution ; Regularizing Property ; Banach Spaces ;

Subject

Probabilidades & matemáticas aplicadas ;

Source link

http://www.ccsenet.org/journal/index.php/jmr/article/view/41409/22688...

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