Isoperimetric inequalities for an ergodic stochastic control problem
In this paper we deal with blow-up solutions to an elliptic equation with a nonlinear gradient term. The problem under consideration can be seen as the ergodic limit of a stochastic control problem with state constraints. It is well known that it has a solution only when a parameter which appears in...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2013-03, Vol.46 (3-4), p.749-768 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Ferone, Vincenzo Giarrusso, Ester Messano, Basilio Posteraro, M. Rosaria |
| description | In this paper we deal with blow-up solutions to an elliptic equation with a nonlinear gradient term. The problem under consideration can be seen as the ergodic limit of a stochastic control problem with state constraints. It is well known that it has a solution only when a parameter which appears in the equation assumes a particular value known as
ergodic constant
. For such a constant many properties similar to those of an eigenvalue hold true. We show that a Faber–Krahn inequality can be stated for the ergodic constant and that for the corresponding solution a comparison result in terms of the solution to a symmetrized problem can be proved. |
| doi_str_mv | 10.1007/s00526-012-0502-7 |
| format | Article |
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ergodic constant
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ergodic constant
. For such a constant many properties similar to those of an eigenvalue hold true. 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ergodic constant
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| source | Springer Nature - Complete Springer Journals |
| subjects | Analysis Calculus of variations Calculus of Variations and Optimal Control Optimization Control Eigenvalues Ergodic processes Inequalities Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonlinear equations Nonlinearity Partial differential equations Stochastic models Stochasticity Systems Theory Theoretical |
| title | Isoperimetric inequalities for an ergodic stochastic control problem |
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