Lipschitz bounds for nonuniformly elliptic integral functionals in the plane
M Schäffner - arXiv preprint arXiv:2402.06252, 2024 - arxiv.org
We study local regularity properties of local minimizer of scalar integral functionals with
controlled $(p, q) $-growth in the two-dimensional plane. We establish Lipschitz continuity …
controlled $(p, q) $-growth in the two-dimensional plane. We establish Lipschitz continuity …
Nonlinear potential theoretic methods in nonuniformly ellliptic problems
G Mingione - arXiv preprint arXiv:2402.02683, 2024 - arxiv.org
Nonuniform ellipticity is a classical topic in the theory of partial differential equations. While
several results in regularity theory have been adding up over decades, many basic issues …
several results in regularity theory have been adding up over decades, many basic issues …
Discarding Lavrentiev's Gap in Non-automonous and Non-Convex Variational Problems
M Borowski, P Bousquet, I Chlebicka, B Lledos… - arXiv preprint arXiv …, 2024 - arxiv.org
We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur
for a scalar variational problem of the form:\[\textrm {to minimize}\qquad …
for a scalar variational problem of the form:\[\textrm {to minimize}\qquad …