Year: 2024
Type: preprint
Abstract: We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $\mathrm{BD}(Ω)$ have weak gradients in $\mathrm{L}_{\mathrm{loc}}^{1}(Ω;\mathbb{R}^{n\times n})$. This is achieved for the sharp ellipticity range that is presently known to yield $\mathrm{W}_{\mathrm{loc}}^{1,1}$-regularity in the full gradient case on $\mathrm{BV}(Ω;\mathbb{R}^{n})$. As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on $\mathrm{BD}(Ω)$.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Hector Stiftung
Award: G6996040285
OpenAlex ID: W4405716292