87 citations · 96 across the 4 of their papers we have counts for
6 papers
Sharp Higher Integrability Theory, Part I: The -norm of the Beurling--Ahlfors transform
Andrea Agazzi, Kari Astala, Giuseppe Bruno +18
We confirm a conjecture posed by T. Iwaniec in 1982: the norm of the Beurling--Ahlfors transform is if , and if .
Geometric measure theory and differential inclusions
Camillo De Lellis, Guido De Philippis, Bernd Kirchheim +1
In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifold…
Two-by-two upper triangular matrices and Morrey's conjecture
Terence L. J. Harris, Bernd Kirchheim, Chun-Chi Lin
It is shown that every homogeneous gradient Young measure supported on matrices of the form $\begin{pmatrix} a_{1,1} & \cdots & a_{1,n-1} & a_{1,n} \\ 0 & \cdots & 0 & a_{2,n} \end…
On Rank-One Convex Functions that are homogeneous of Degree One
Bernd Kirchheim, Jan Kristensen
We show that positively --homogeneous rank one convex functions are convex at and at matrices of rank one. The result is a special case of an abstract convexity result that…
Square Functions and the Property of Elliptic Measures
C. Kenig, B. Kirchheim, J. Pipher +1
In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric dive…
Equidimensional isometric maps
Bernd Kirchheim, Emanuele Spadaro, Laszlo Szekelyhidi
In Gromov's treatise Partial Differential Relations (volume 9 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 1986), a continuous map between Riemannian manifolds is calle…