Abstract We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on BD () BD (Ω) have weak gradients in L₋₎₂^1 (; R^n n) L loc 1 (Ω ; R n × n). This is achieved for the sharp ellipticity range that is presently known to yield W₋₎₂^1, 1 W loc 1, 1 -regularity in the full gradient case on BV (; R^n) BV (Ω ; R n). As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on BD () BD (Ω).
Beck et al. (Mon,) studied this question.