Jan Kristensen

activity

20102026

most citedOn Rank-One Convex Functions that are homogeneous of Degree One

87 citations · 190 across the 16 of their papers we have counts for

collaborators

18 papers

math.CV2026

Sharp Higher Integrability Theory, Part I: The $L^{p}$ -norm of the Beurling--Ahlfors transform

Andrea Agazzi, Kari Astala, Giuseppe Bruno +18

We confirm a conjecture posed by T. Iwaniec in 1982: the $L^{p}$ norm of the Beurling--Ahlfors transform is $p - 1$ if $p \geq 2$ , and $(p - 1)^{- 1}$ if $1 < p \leq 2$ .

math.AP2022★ 1 cited

$A$ -harmonic approximation and partial regularity, revisited

Matthias Bärlin, Franz Gmeineder, Christopher Irving +1

We give a direct harmonic approximation lemma for local minima of quasiconvex multiple integrals that entails their $C^{1, α}$ or $C^{\infty}$ -partial regularity.…

math.AP2022★ 1 cited

Quasiconvex functionals of $(p, q)$ -growth and the partial regularity of relaxed minimizers

Franz Gmeineder, Jan Kristensen

We establish $C^{\infty}$ -partial regularity results for relaxed minimizers of strongly quasiconvex functionals \begin{align*} \mathscr{F}[u;Ω]:=\int_ΩF(\nabla u)\,\mathrm…

math.AP2022

Distortion of Hausdorff measures under Orlicz--Sobolev maps

Andrea Cianchi, Mikhail V. Korobkov, Jan Kristensen

A comprehensive theory of the effect of Orlicz-Sobolev maps, between Euclidean spaces, on subsets with zero or finite Hausdorff measure is offered. Arbitrary Orlicz-Sobolev spaces…

math.AP2022★ 1 cited

On the validity of the Euler-Lagrange system without growth assumptions

Lukas Koch, Jan Kristensen

The constrained minimisers of convex integral functionals of the form $F (v) = \int_{Ω} F (\nabla^{k} v (x)) d x$ defined on Sobolev mappings $v\in \mathrm W^{k,1}_g(Ω, \mat…

math.AP2021

Concentration effects of BV gradients have gradient structure

Jan Kristensen, Bogdan Raiţă

We prove that the concentration effects arising from weakly-* convergent sequences of gradients of maps of bounded variation have gradient structure. This is in stark contrast with…

math.AP2021

Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands

André Guerra, Jan Kristensen

We consider the class of non-negative rank-one convex isotropic integrands on $R^{n \times n}$ which are also positively $p$ -homogeneous. If $p \leq n = 2$ we prove, condit…

math.AP2019★ 13 cited

Oscillation and concentration in sequences of PDE constrained measures

Jan Kristensen, Bogdan Raiţă

We show that for constant rank partial differential operators $A$ , generalized Young measures generated by sequences of $A$ -free measures can be characterized b…

math.AP2019★ 1 cited

Regularity for higher order quasiconvex problems with linear growth from below

Franz Gmeineder, Jan Kristensen

We announce new existence and $ε$ -regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps $u\colonΩ\subset\mathbb{R}^{n}…

math.AP2018★ 34 cited

Partial Regularity for BV Minimizers

Franz Gmeineder, Jan Kristensen

We establish an $ε$ -regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, a…

math.AP2016

Sobolev regularity for Convex Functionals on BD

Franz Gmeineder, Jan Kristensen

We study Sobolev regularity results for minimisers of autonomous, convex variational of linear growth which depend on the symmetric gradient rather than the full gradient. This ext…

math.AP2016★ 13 cited

A bridge between Dubovitskii - Federer theorems and the coarea formula

Piotr Hajlasz, Mikhail V. Korobkov, Jan Kristensen

The Morse-Sard theorem requires that a mapping $v : R^{n} \to R^{m}$ is of class $C^{k}$ , $k > n - m$ . In 1957 Dubovitski\uı generalized this result by proving that almost all level sets for a…

math.FA2015

Lower semicontinuity for an integral functional in BV

Jan Kristensen, Panu Lahti

We prove a lower semicontinuity result for a functional of linear growth initially defined by \[ \int_ΩF\left(\frac{dDu}{dμ}\right)\,dμ\] for $u \in B V (Ω; R^{N})$ with $Du\ll…

math.AP2015★ 87 cited

On Rank-One Convex Functions that are homogeneous of Degree One

Bernd Kirchheim, Jan Kristensen

We show that positively $1$ --homogeneous rank one convex functions are convex at $0$ and at matrices of rank one. The result is a special case of an abstract convexity result that…

math.AP2013★ 38 cited

Regularity of minimizers of autonomous convex variational integrals

Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli

We establish local higher integrability and differentiability results for minimizers of variational integrals $F (v, Ω) = \int_{Ω} /! F (D v (x)) d x$ over $W^{1, p}$ --Sob…

math.AP2012★ 1 cited

Piecewise affine approximations for functions of bounded variation

Jan Kristensen, Filip Rindler

BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine func…

math.AP2012

On the Morse-Sard property and level sets of $W^{n, 1}$ Sobolev functions on $R^{n}$

Jean Bourgain, Mikhail V. Korobkov, Jan Kristensen

We establish Luzin N and Morse--Sard properties for functions from the Sobolev space $W^{n, 1} (R^{n})$ . Using these results we prove that almost all level sets are finite…

math.AP2010

On the Morse-Sard Property and Level Sets of Sobolev and BV Functions

Jean Bourgain, Mikhail V. Korobkov, Jan Kristensen

We establish Luzin $N$ and Morse-Sard properties for $B V_{2}$ -functions defined on open domains in the plane. Using these results we prove that almost all level sets are finite disjo…

Sharp Higher Integrability Theory, Part I: The Lp-norm of the Beurling--Ahlfors transform

A-harmonic approximation and partial regularity, revisited

Quasiconvex functionals of (p,q)-growth and the partial regularity of relaxed minimizers

Distortion of Hausdorff measures under Orlicz--Sobolev maps

On the validity of the Euler-Lagrange system without growth assumptions

Concentration effects of BV gradients have gradient structure

Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands

Oscillation and concentration in sequences of PDE constrained measures

Regularity for higher order quasiconvex problems with linear growth from below

Partial Regularity for BV Minimizers

Sobolev regularity for Convex Functionals on BD

A bridge between Dubovitskii - Federer theorems and the coarea formula

Lower semicontinuity for an integral functional in BV

On Rank-One Convex Functions that are homogeneous of Degree One

Regularity of minimizers of autonomous convex variational integrals

Piecewise affine approximations for functions of bounded variation

On the Morse-Sard property and level sets of Wn,1 Sobolev functions on Rn

On the Morse-Sard Property and Level Sets of Sobolev and BV Functions

Sharp Higher Integrability Theory, Part I: The $L^{p}$ -norm of the Beurling--Ahlfors transform

$A$ -harmonic approximation and partial regularity, revisited

Quasiconvex functionals of $(p, q)$ -growth and the partial regularity of relaxed minimizers

On the Morse-Sard property and level sets of $W^{n, 1}$ Sobolev functions on $R^{n}$