Some singular minimizers in low dimensions in the calculus of variations

Abstract

We construct a singular minimizing map $\mathbf{u}$ from ${\mathbb{R}}^3$ to ${\mathbb{R}}^2$ of a smooth uniformly convex functional of the form ${\int }_{B_1}F(D\mathbf{u})dx$.

19 pages, 8 figures

References in corpus (1)

• Minimizers of Convex Functionals Arising in Random Surfaces

Cited by in corpus (3)

• Partial Regularity for BV Minimizers
• Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth
• Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem