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Media type:
E-Article
Title:
Free Boundary Regularity Close to Initial State for Parabolic Obstacle Problem
Contributor:
Shahgholian, Henrik
Published:
American Mathematical Society, 2008
Published in:
Transactions of the American Mathematical Society, 360 (2008) 4, Seite 2077-2087
Language:
English
ISSN:
0002-9947
Origination:
Footnote:
Description:
In this paper we study the behavior of the free boundary ∂ {u &gt ψ}, arising in the following complementary problem: $ \matrix\format\c\\ (Hu)(u-\psi)=0,\quad u\geq \psi (x,t)\ \text{in}\quad Q^{+}, \\ Hu\leq 0, \\ u(x,t)\geq \psi (x,t)\quad \text{on}\quad \partial _{p}Q^{+} \endmatrix $. Here $\partial _{p}$ denotes the parabolic boundary, H is a parabolic operator with certain properties, Q⁺ is the upper half of the unit cylinder in ${\bf R}^{n+1}$, and the equation is satisfied in the viscosity sense. The obstacle ψ is assumed to be continuous (with a certain smoothness at {x₁ = 0, t = 0}), and coincides with the boundary data u(x, 0) = ψ(x, 0) at time zero. We also discuss applications in financial markets.