论文信息 - An optimal Poincare inequality in L^1 for convex domains

An optimal Poincare inequality in L^1 for convex domains

For convex domains Ω C R n with diameter d we prove ∥u∥ L 1 (ω) ≤ d 2 ∥⊇ u ∥ L 1 (ω) for any u with zero mean value on w. We also show that the constant 1/2 in this inequality is optimal.

Ricardo G. Durán | R. Durán | Gabriel Acosta | Gabriel Acosta

[1] Rüdiger Verfürth,et al. A note on polynomial approximation in Sobolev spaces , 1999 .

[2] S. Agmon. Lectures on Elliptic Boundary Value Problems , 1965 .

[3] V. V. Buldygin,et al. Brunn-Minkowski inequality , 2000 .

[4] H. Weinberger,et al. An optimal Poincaré inequality for convex domains , 1960 .

[5] P. Bassanini,et al. Elliptic Partial Differential Equations of Second Order , 1997 .