Analysis of a Degenerate Obstacle Problem on an Unbounded Set Arising in the Environment
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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.
- Analysis of a Degenerate Obstacle Problem on an Unbounded Set Arising in the Environment
Applied Mathematics & Optimization
Volume 45, Issue 3 , pp 251-267
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- Key words. Elliptic free boundary, Degenerate operator, Unbounded domain, Environmental policy. AMS Classification. 35J85, 35J70, 35R35, 91B76, 93E20.