Applied Mathematics & Optimization

, Volume 45, Issue 3, pp 251–267

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

  •  Díaz
  •  Faghloumi

DOI: 10.1007/s00245-001-0038-2

Cite this article as:
Díaz & Faghloumi Appl Math Optim (2002) 45: 251. doi:10.1007/s00245-001-0038-2

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.

Key words. Elliptic free boundary, Degenerate operator, Unbounded domain, Environmental policy. AMS Classification. 35J85, 35J70, 35R35, 91B76, 93E20. 

Copyright information

© 2002 Springer-Verlag New York Inc.

Authors and Affiliations

  •  Díaz
    • 1
  •  Faghloumi
    • 1
  1. 1.Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain {JI_Diaz,Chakib_Faghloumi}@mat.ucm.es Communicated by A. BensoussanES