An optimal Poincaré inequality in L1 for convex domains
For convex domains Ω ⊂ ℝn with diameter d we prove ||u||L1(ω) ≤ d/2||∇u||L1(ω) for any u with zero mean value on ω. We also show that the constant 1/2 in this inequality is optimal.
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029939_v132_n1_p195_Acosta |
| Aporte de: |
| Sumario: | For convex domains Ω ⊂ ℝn with diameter d we prove ||u||L1(ω) ≤ d/2||∇u||L1(ω) for any u with zero mean value on ω. We also show that the constant 1/2 in this inequality is optimal. |
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