21 citations · 141 across the 22 of their papers we have counts for
23 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 .
Homogenization of iterated singular integrals with applications to random quasiconformal maps
Kari Astala, Steffen Rohde, Eero Saksman +1
We study homogenization of iterated randomized singular integrals and homeomorphic solutions to the Beltrami differential equation with a random Beltrami coefficient. More precisel…
Dimer Models and Conformal Structures
Kari Astala, Erik Duse, István Prause +1
In this work we study the variational problem associated to dimer models, a class of models from integrable probability and statistical mechanics in dimension two which have been t…
Improved Hölder regularity for strongly elliptic PDEs
Kari Astala, Albert Clop, Daniel Faraco +2
We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the non…
Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
Kari Astala, Martí Prats, Eero Saksman
We study quasiconformal mappings in planar domains and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to opt…
Nonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian
Kari Astala, Albert Clop, Daniel Faraco +2
We provide Schauder estimates for nonlinear Beltrami equations and lower bounds of the Jacobians for homeomorphic solutions. The results were announced in arXiv:1412.4046 but here…