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Stability Estimates for the Elliptic and Parabolic Obstacle Problems

Thesis Info

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Author

Naveed Ahmad

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1783

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727230873

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Stability of the solution of the multidimensional unilateral obstacle problem with respect to the variations of the coefficients of the corresponding second order partial differential operator is studied in the present thesis. A H ̈lder type stability estimate in the second order Sobolev space of functions is o established for the solution of the elliptic obstacle problem. Rodrigues ([25, 1987]) proved the stability result with respect to bounded external force functions under the nondegeneracy condition. We generalize this result to the case of arbitrary functions belonging to the space Lp (D), p ≥ 2. Further parabolic obstacle problem is studied with different principal parts in the parabolic differential operator and applied to the American put option problem with various local volatility functions. The estimate of the area between the early exercise boundaries through the uniform distance between the local volatility functions is obtained.
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