A Hadamard-jensen inequality and an application to the elastic torsion problem
نویسندگان
چکیده
منابع مشابه
Generalisation of Hadamard’s inequality for convex functions to higher dimensions, and an application to the elastic torsion problem
The (generalised) torsion function u of a domain Ω ⊂ IR is a function which is zero on the boundary of the domain and whose Laplacian is minus one at every point in the interior of the domain. Denote by |Ω| the measure of Ω, xc its centroid. We establish, for convex Ω, 3 2(n+ 1)2 ≤ 1 (n + 1)2 |Ω| ∫ Ω u max Ω u ≤ |Ω|u(xc) ∫ Ω u ≤ |Ω| ∫ Ω u max Ω u ≤ 1 2 (n+ 1)(n+ 2). We generalise this to positi...
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ژورنال
عنوان ژورنال: Applicable Analysis
سال: 2000
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036810008840849