A compactness result in $$GSBV^p$$ G S B V p and applications to $$\varGamma $$ Γ -convergence for free discontinuity problems
作者： Manuel Friedrich
DOI: 10.1007/S00526-019-1530-3
关键词:
摘要: We present a compactness result in the space $$GSBV^p$$ which extends classical statement due to Ambrosio (Arch Ration Mech 111:291–322, 1990) problems without priori bounds on functions. As an application, we revisit $$\varGamma $$ -convergence results for free discontinuity functionals established recently by Cagnetti et al. [Ann Inst H Poincare Anal Non Lineaire (to appear)]. investigate sequences of boundary value and show convergence minimum values minimizers.
springer.com
sci-hub.se 参考文章(38)
Guido Cortesani, Strong approximation ofGSBV functions by piecewise smooth functions Annali Dell'universita' Di Ferrara. ,vol. 43, pp. 27- 49 ,(1997) , 10.1007/BF02837227
Andrea Braides, Γ-convergence for beginners Oxford University Press. ,(2002)
Diego Pallara, Luigi Ambrosio, Nicola Fusco, Functions of Bounded Variation and Free Discontinuity Problems ,(2000)
G.I. Barenblatt, THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE Advances in Applied Mechanics. ,vol. 7, pp. 55- 129 ,(1962) , 10.1016/S0065-2156(08)70121-2
Marcello Ponsiglione, Gianni Dal Maso, Alessandro Giacomini, A VARIATIONAL MODEL FOR QUASISTATIC CRACK GROWTH IN NONLINEAR ELASTICITY: SOME QUALITATIVE PROPERTIES OF THE SOLUTIONS Bollettino Della Unione Matematica Italiana. ,vol. 2, pp. 371- 390 ,(2009)
Marcello Ponsiglione, Alessandro Giacomini, A $\Gamma$-convergence approach to stability of unilateral minimality properties arXiv: Analysis of PDEs. ,(2005)
Antonin Chambolle, A Density Result in Two-Dimensional Linearized Elasticity, and Applications Archive for Rational Mechanics and Analysis. ,vol. 167, pp. 211- 233 ,(2003) , 10.1007/S00205-002-0240-7
G. Bellettini, A. Coscia, G. Dal Maso, Compactness and lower semicontinuity properties in SBD(Omega) Mathematische Zeitschrift. ,vol. 228, pp. 337- 351 ,(1998) , 10.1007/PL00004617
A. A. Griffith, The Phenomena of Rupture and Flow in Solids Philosophical Transactions of the Royal Society A. ,vol. 221, pp. 163- 198 ,(1921) , 10.1098/RSTA.1921.0006
Filippo Cagnetti, Rodica Toader, Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach ESAIM: Control, Optimisation and Calculus of Variations. ,vol. 17, pp. 1- 27 ,(2011) , 10.1051/COCV/2009037