Quasiconvexification in W 1,1 and Optimal Jump Microstructure in BV Relaxation
Christopher J. Larsen · SIAM Journal on Mathematical Analysis · 1998
An integral representation for the relaxation in $BV(\Omega;\rn{p})$ of the functional $$ u \mapsto \io W( abla u(x)) dx +\hn(S(u)) $$ with respect to BV weak * convergence is obtained. The bulk term in the integral representation reduces to the quasiconvexification of W, and we describe optimal behavior of approximating sequences along S(u), for scalar valued u.