Geodesic
Stability of the coincidence set of a~solution to a~parabolic variational inequality with an obstacle
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 88-91.

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In this paper we propose a new technique for the stability analysis of the coincidence set of a solution to a parabolic variational inequality with an obstacle inside the domain. It is based on the reformulation of the initial inequality in the form of a parabolic initial boundary value problem with an exact penalty operator.
Keywords: variational inequality, obstacle problem, coincidence set, stability, capacity. 
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A. I. Mikheeva; R. Z. Dautov. Stability of the coincidence set of a~solution to a~parabolic variational inequality with an obstacle. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 88-91. http://geodesic.mathdoc.fr/item/IVM_2010_3_a10/

[1] Fridman A., Variatsionnye printsipy i zadachi so svobodnoi granitsei, Mir, M., 1990, 536 pp. | MR

[2] Caffarelli L. A., “A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets”, Boll. Un. Mat. Ital. A, 18:1 (1981), 109–113 | MR | Zbl

[3] Lee K., Shahgholian H., “Hausdorff dimension and stability of the $p$-obstacle problem ($2

$)”, J. Differential Equations, 195:1 (2003), 14–24 | DOI | MR | Zbl

[4] Mikheeva A. I., Dautov R. Z., “O tochnosti metoda shtrafa dlya parabolicheskikh variatsionnykh neravenstv s prepyatstviem vnutri oblasti”, Izv. vuzov. Matematika, 2008, no. 2, 41–47 | MR