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Analysis of a degenerate obstacle problem on an unbounded set arising in the environment

Díaz Díaz, Jesús Ildefonso and Faghloumi, Ch. (2002) Analysis of a degenerate obstacle problem on an unbounded set arising in the environment. Applied Mathematics & Optimization, 45 (3). pp. 251-267. ISSN 0095-4616

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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.

Item Type:Article
Uncontrolled Keywords:elliptic free boundary; degenerate operator; unbounded domain; environmental policy
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Differential equations
ID Code:15524
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