ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Wang, Hwai-chiuan, Tsing Hua University, Taiwan Semilinear Elliptic Problems in Interior and Exterior Flask Domains. In this note we prove the following assertions: (1) α_{I} = α_{M} = α_{Γ}; (2) let Ω_{0} = Ω_{1} ∪ Ω_{2}, where Ω_{1} ∩ Ω_{2} is bounded, and α_{i} = α(Ω_{i}) the index of J in Ω_{i} for i = 0, 1, 2. J satisfies the (P S)_{α_{0}}- condition if and only if the inequality α_{0} < min{α_{1}, α_{2}} holds; (3) there exists s_{0} > 0 such that α(D_{s}^{r}) admits a minimizer if s > s_{0}, but α(D_{s}^{r}) does not admit any minimizer if s < s_{0}, where D_{s}^{r} is an interior flask domain.