Free boundary regularity close to initial state for parabolic obstacle problem
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- by Henrik Shahgholian PDF
- Trans. Amer. Math. Soc. 360 (2008), 2077-2087 Request permission
Abstract:
In this paper we study the behavior of the free boundary $\partial \{u>\psi \}$, arising in the following complementary problem: \begin{gather*} (Hu)(u-\psi )=0,\qquad u\geq \psi (x,t) \quad \mathrm {in}\ Q^+, Hu \leq 0, u(x,t) \geq \psi (x,t) \quad \mathrm {on}\ \partial _p Q^+. \end{gather*} 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 $\textbf {R}^{n+1}$, and the equation is satisfied in the viscosity sense. The obstacle $\psi$ is assumed to be continuous (with a certain smoothness at $\{x_1=0$, $t=0\}$), and coincides with the boundary data $u(x,0)=\psi (x,0)$ at time zero. We also discuss applications in financial markets.References
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Additional Information
- Henrik Shahgholian
- Affiliation: Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
- Email: henriksh@math.kth.se
- Received by editor(s): January 7, 2005
- Received by editor(s) in revised form: February 19, 2006
- Published electronically: November 19, 2007
- Additional Notes: This work was supported in part by the Swedish Research Council.
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 2077-2087
- MSC (2000): Primary 35R35
- DOI: https://doi.org/10.1090/S0002-9947-07-04292-4
- MathSciNet review: 2366975