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March/April 2015 Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
Paul M.N. Feehan, Camelia A. Pop
Adv. Differential Equations 20(3/4): 361-432 (March/April 2015).

Abstract

We establish higher-order weighted Sobolev and Hölder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance [27]. Furthermore, given $C^\infty$-smooth data, we prove $C^\infty$-regularity of solutions up to the portion of the boundary where the operator is degenerate. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset.

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Paul M.N. Feehan. Camelia A. Pop. "Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations." Adv. Differential Equations 20 (3/4) 361 - 432, March/April 2015.

Information

Published: March/April 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1311.35322
MathSciNet: MR3311437

Subjects:
Primary: 35J70 , 35R45 , 49J40 , 60J60

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 3/4 • March/April 2015
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