Let u be a solution to the obstacle problem\(u \geqslant 0, - \Delta u + f \geqslant 0,u( - \Delta u + f) = 0\) in a domain Ω⊂ℝn. In this paper, the behavior of the free boundary in a neighborhood of ϖΩ is studied. It is proved that under some conditions the free boundary touches ϖΩ at contact points. Bibliography:4 titles.
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O. A. Ladyzhenskaya and N. N. Uraltseva,Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 5–19.
Translated by T. N. Rozhkovskaya.
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Apushkinskaya, D.E., Uraltseva, N.N. On the behavior of free boundaries near the boundary of the domain. J Math Sci 87, 3267–3276 (1997). https://doi.org/10.1007/BF02355579
- Contact Point
- Free Boundary
- Obstacle Problem
- Boundary Touch