Integral Representation for Functionals Defined on SBD^p in Dimension Two

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• 作者：Sergio Conti ; Matteo Focardi…
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：223
• 期：3
• 页码：1337-1374
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0673
• 卷排序：223

文摘

We prove an integral representation result for functionals with growth conditions which give coercivity on the space \({SBD^p(\Omega)}\), for \({\Omega\subset\mathbb{R}^{2}}\), which is a bounded open Lipschitz set, and \({p\in(1,\infty)}\). The space SBDp of functions whose distributional strain is the sum of an Lp part and a bounded measure supported on a set of finite \({\mathcal{H}^{1}}\)-dimensional measure appears naturally in the study of fracture and damage models. Our result is based on the construction of a local approximation by W1,p functions. We also obtain a generalization of Korn’s inequality in the SBDp setting.