Abstract We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $$\textrm{BD}(\Omega )$$ <mml:math xmlns:mml="http://www.
We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on BD(Ω ) BD ( Ω ) have weak gradients in Lloc¹(Ω ;Rn× n) L loc 1 ( Ω ; R n × n ) . This is achieved for the sharp ellipticity range that is presently known to yield Wloc1,1 W loc 1 , 1 -regularity in the full gradient case on BV(Ω ;Rⁿ) BV ( Ω ; R n ) . As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on BD(Ω ) BD ( Ω ) .
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Beck et al. (2026) studied this question.
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