Backward Ornstein-Uhlenbeck Transition Operators and Mild Solutions of Non-Autonomous Hamilton-Jacobi Equations in Banach Spaces
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...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2014
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/14405
- Acceso en línea:
- http://repository.urosario.edu.co/handle/10336/14405
- Palabra clave:
- Ornstein-Uhlenbeck Processes
Infinite-Dimensional Hamilton-Jacobi Equations
Mild Solution
Regularizing Property
Banach Spaces
Probabilidades & matemáticas aplicadas
Sistemas estocásticos
Sistemas de Hamilton
- Rights
- License
- Abierto (Texto Completo)
| 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. |
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