Mathematical analysis establishes Sobolev regularity for relaxed minimizers on bounded variation spaces, suggesting sharp extensions for non-uniformly elliptic systems.
We establish W1,1 W 1 , 1 -regularity and higher gradient integrability for relaxed minimizers of convex integral functionals on BV BV . Unlike classical examples such as the minimal surface integrand, we only require linear growth from below but not necessarily from above. This typically comes with a non-uniformly degenerate elliptic behaviour, for which our results extend the presently available bounds from the superlinear growth case in a sharp way.
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Beck et al. (2026) studied this question.
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