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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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Serrano Perdomo, Rafael Antonio
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2014-10-09
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Abstract
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.
Palabras clave
Ornstein-Uhlenbeck Processes , Infinite-Dimensional Hamilton-Jacobi Equations , Mild Solution , Regularizing Property , Banach Spaces
