NONLOCAL KORN-TYPE CHARACTERIZATION OF SOBOLEV VECTOR FIELDS
Abstract
A new nonlocal characterization of Sobolev vector fields in the spirit of Korn's inequality is obtained. As an application of this result, a nonlocal means of identification of rigid motions is given. A nonlocal characterization of vector fields with bounded deformation is also presented. A compactness criteria is proved for bounded sequences of vector fields in Lp.
References
- Numer. Funct. Anal. Optim. 31(12), 1301 (2010). Crossref, ISI, Google Scholar
- J. Elasticity 106(1), 71 (2012). Crossref, ISI, Google Scholar
- Arch. Ration. Mech. Anal. 139, 201 (1997). Crossref, ISI, Google Scholar
-
F. Andreu-Vaillo , Nonlocal Diffusion Problems ,Mathematical Surveys and Monographs 165 ( American Mathematical Society , Providence, RI , 2010 ) . Crossref, Google Scholar - Amer. Math. Monthly 104(1), 36 (1997). Crossref, ISI, Google Scholar
- Optimal Control and Partial Differential Equations, eds.
J. L. Menaldi , E. Rofman and A. Sulem (IOS Press, 2001) pp. 439–455. Google Scholar , -
H. Brézis , Analyse Fonctionnelle. Théorie et Applications ( Masson , 1978 ) . Google Scholar - H. Brézis, How to recognize constant functions. Connections with Sobolev spaces, Uspekhi Mat. Nauk 57 (2002) 59–74 (in Russian); Russian Math. Surveys 57 (2002) 693–708; A volume in honor of M. Vishik . Google Scholar
- Calc. Var. Partial Differential Equations 15, 519 (2002). Crossref, ISI, Google Scholar
- Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, Application of a nonlocal vector calculus to peridynamic modeling, Submitted for publication . Google Scholar
- Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, to appear in Math. Models Methods Appl. Sci . Google Scholar
- ESIAM: Math. Model. Numer. Anal. 45, 217 (2011). Crossref, ISI, Google Scholar
- Math. Model. Anal. 12(1), 17 (2007). Crossref, ISI, Google Scholar
- Commun. Math. Sci. 5(4), 851 (2007). Crossref, ISI, Google Scholar
-
L. C. Evans and R. F. Gariepy , Measure Theory and Fine Properties of Functions ( CRC Press , 1992 ) . Google Scholar - Multiscale Model. Simul. 8, 1581 (2010). Crossref, ISI, Google Scholar
- Ann. Inst. H. Poincaré Anal. Non Linéaire 28(3), 443 (2011). Crossref, ISI, Google Scholar
- J. Mech. Phys. Solids 48, 175 (2000). Crossref, ISI, Google Scholar
-
R. Temam , Problémes Mathématiques en Plasticité ( Gauthier-Villars , Paris , 1983 ) . Google Scholar -
R. Temam and A. Miranville , Mathematical Modeling in Continuum Mechanics ( Cambridge University Press , 2001 ) . Google Scholar - Arch. Ration. Mech. Anal. 75, 7 (1980). Crossref, ISI, Google Scholar
- SIAM J. Numer. Anal. 48, 1759 (2010). Crossref, ISI, Google Scholar
Remember to check out the Most Cited Articles! |
---|
Be inspired by these NEW Mathematics books for inspirations & latest information in your research area! |