Upper bounds for singular perturbation problems involving gradient fields

  • Arkady Poliakovsky

    Technion - Israel Institute of Technology, Haifa, Israel

Abstract

We prove an upper bound for the Aviles–Giga problem, which involves the minimization of the energy over , where is a small parameter. Given such that and a.e., we construct a family satisfying: in and , as goes to .

Cite this article

Arkady Poliakovsky, Upper bounds for singular perturbation problems involving gradient fields. J. Eur. Math. Soc. 9 (2007), no. 1, pp. 1–43

DOI 10.4171/JEMS/70