Regularity for minimizers with positive Jacobian. Issue 3 (17th February 2020) - Gao, Hongya; Leonetti, Francesco; Macrì, Marta; Petricca, Pier Vincenzo
ABSTRACT: We deal with maps u : Ω ⊂ R n → R n minimizing variational integrals ∫ Ω [ | D u ( x ) | p + h ( det D u ( x ) ) ] d x, where 2 ≤ p < n, h : ( 0, + ∞ ) → [ 0, + ∞ ) is convex and blows when det D u → 0 + : lim t → 0 + h ( t ) = + ∞ . If such a blow up is a power of | ln ⁡ ( t ) |, then we derive regularity for the minimizer u = ( u 1, …, u n ) . We are able also to deal with integrals containing all the minors: ∫ Ω [ | D u ( x ) | p + ∑ s = 2 n − 1 | adj s ( D u ( x ) ) | q s + h ( det D u ( x ) ) ] d x with q s ≥ 1 .