Analysis of blow-ups for the double obstacle problem in dimension two

  • Gohar Aleksanyan

    KTH Royal Institute of Technology, Stockholm, Sweden
Analysis of blow-ups for the double obstacle problem in dimension two cover

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Abstract

In this article we study a normalised double obstacle problem with polynomial obstacles , where the equality holds iff . In dimension two we give a complete classification of blow-up solutions. In particular, we see that there exists a new type of blow-ups, which we call double-cone solutions, since the coincidence sets and are cones with a common vertex. Furthermore, we show that if the solution to the double obstacle problem has a double-cone blow-up limit at the origin, then the blow-up is unique, and locally the free boundary consists of four -curves, meeting at the origin.

Cite this article

Gohar Aleksanyan, Analysis of blow-ups for the double obstacle problem in dimension two. Interfaces Free Bound. 21 (2019), no. 2, pp. 131–167

DOI 10.4171/IFB/419