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Analysis of a Degenerate Obstacle Problem on an Unbounded Set Arising in the Environment

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Abstract.

We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form. The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set.

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  1. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain {JI_Diaz,Chakib_Faghloumi}@mat.ucm.es Communicated by A. Bensoussan, , , , , , ES

    Díaz &  Faghloumi

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  1. Díaz
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  2. Faghloumi
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Díaz, ., Faghloumi, . Analysis of a Degenerate Obstacle Problem on an Unbounded Set Arising in the Environment . Appl Math Optim 45, 251–267 (2002). https://doi.org/10.1007/s00245-001-0038-2

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  • DOI: https://doi.org/10.1007/s00245-001-0038-2

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