Regularity for higher order quasiconvex problems with linear growth from below

2019/03/19 by Franz Gmeineder, Gmeineder, Franz, Jan Kristensen +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Applied mathematics #Convex analysis #Economics #FOS: Mathematics #Geometry #Mathematical economics #Mathematics #Nonlinear Partial Differential Equations #Order (exchange) #Quasiconvex function #Regular polygon #math.AP

paper · pdf · doi:10.48550/arxiv.1903.08124

Announcement, 5 pages

arxiv created 2019/03/19 · openalex publication_date 2019/03/19 · arxiv updated 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We announce new existence and ε-regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps u\colonΩ⊂ℝⁿ→ℝ^N are defined by u↦ ∫_ΩF(∇^ku)dx. The results cover the case of integrands F with (1,q)-growth in the full range of exponents 1<q<(n)/(n-1) for which a measure representation of the relaxed functional is possible and the minimizers belong to the space BV^k of maps whose k-th order derivatives are measures.

Cited by

• A Class of De Giorgi Type and Hölder Continuity for Some Problems in Musielak-Orlicz-Sobolev Spaces

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