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arXiv · 1903.08124

Regularity for higher order quasiconvex problems with linear growth from below

Franz Gmeineder·Jan Kristensen
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Abstract

We announce new existence and $\varepsilon$-regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps $u\colon\Omega\subset\mathbb{R}^{n}\to\mathbb{R}^{N}$ are defined by $$u\mapsto \int_{\Omega}F(\nabla^{k}u)dx.$$ The results cover the case of integrands $F$ with $(1,q)$-growth in the full range of exponents $1<q<\frac{n}{n-1}$ 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.

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Franz Gmeineder, Jan Kristensen. 2019-03-19. Regularity for higher order quasiconvex problems with linear growth from below. https://arxiv.org/abs/1903.08124

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