6533b853fe1ef96bd12ac387

RESEARCH PRODUCT

Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems of Fracture Mechanics

Giuliano GargiuloElvira Zappale

subject

Mathematics - Analysis of PDEsFOS: MathematicsFOS: Physical sciences49J45 74A45 74R10Mathematical Physics (math-ph)Mathematical PhysicsAnalysis of PDEs (math.AP)

description

We provide some lower semicontinuity results in the space of special functions of bounded deformation for energies of the type $$ %\int_\O {1/2}({\mathbb C} \E u, \E u)dx + \int_{J_{u}} \Theta(u^+, u^-, \nu_{u})d \H^{N-1} \enspace, \enspace [u]\cdot \nu_u \geq 0 \enspace {\cal H}^{N-1}-\hbox{a. e. on}J_u, $$ and give some examples and applications to minimum problems. \noindent Keywords: Lower semicontinuity, fracture, special functions of bounded deformation, joint convexity, $BV$-ellipticity.

https://dx.doi.org/10.48550/arxiv.0912.5131