Analysis of Slender Reinforced Concrete Frames - download pdf or read online

By Knut Aas-Jakobsen, Mathis Grenacher (auth.)

ISBN-10: 3034859767

ISBN-13: 9783034859769

ISBN-10: 3764307315

ISBN-13: 9783764307318

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Appl. Math. Sci. 147, SpringerVerlag, New York, 2006. [3] M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, Bristol, 1998. 860 GILLES AUBERT AND PIERRE KORNPROBST [4] D. P. , Athena Scientific, Nashua, NH, 1999. [5] J. Bourgain, H. Brezis, and P. Mironescu, Another look at Sobolev spaces, in Optimal Control and Partial Differential Equations, J. L. Menaldi, E. Rofman, and A. , IOS Press, 2001, pp. 439–455. [6] A. Buades, B. Coll, and J. M.

In this article we propose an alternative method based on a recent new characterization of the Sobolev spaces by Bourgain, Brezis, and Mironescu [5], and further extended by Ponce [16] in the BV -case. In [5] the authors showed that the Sobolev seminorm of a function f can be approximated by a sequence of integral operators involving a differential quotient of f and a suitable sequence of radial mollifiers: lim n→∞ Ω Ω |u(x) − u(y)|p ρn (|x − y|)dxdy = KN,p |x − y|p |∇u|p dx. Ω ∗ Received by the editors July 10, 2007; accepted for publication (in revised form) October 15, 2008; published electronically February 6, 2009.

Regularity result for un . We have obtained the existence of a minimizer in Lp (Ω). Let us show that the solution is in fact more regular than just Lp . As for W 1,p (Ω), the space W s,p (Ω) can be characterized by a differential quotient. For 0 < s < 1 and 1 ≤ p < ∞, we define W s,p (Ω) = u ∈ Lp (Ω); |u(x) − u(y)| ∈ Lp (Ω × Ω) , |x − y|s+N/p endowed with the norm |u|pW s,p (Ω) = |u|p dx + Ω Ω Ω |u(x) − u(y)|p dxdy. , C(n) may be different from one line to the next). 10) Ω Ω |uln (x) − uln (y)|p ρn (|x − y|)dxdy ≤ C(n).

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Analysis of Slender Reinforced Concrete Frames by Knut Aas-Jakobsen, Mathis Grenacher (auth.)


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