ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 34, 35, 46 Bouguima, Sidi Mohammed, University of Tlemcen, Algeria: (*) Free boundary problem in the plane In this lecture, we consider the existence of solutions of the Free bondary problem of the following type:

\{ \begin{matrix}−Δu = λg(u) inΩ \\ u = h onδΩ \end{matrix} \} .

where Ω is unitil ball in ℜ^{2} , g : ℜ → ℜ is a function which can be discontinuous. Under suitable hypotheses, we show that there exist λ^{∗} such that for all λ > λ∗, there exist two solutions and we characterize their free boundaries:

{x ∈ Ω : u(x) = 1}

The value λ∗ is a critical value where possible bifurcation occurs. (*) This work is done jointly with A. Boucherif.