Aleksis Koski

activity

20152026

most citedNonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian

14 citations · 27 across the 14 of their papers we have counts for

collaborators

16 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.CV2025

Characterizing Sobolev Homeomorphic Extensions via Internal Distances

Aleksis Koski, Jani Onninen, Haiqing Xu

We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasicon…

math.AP2024

Lower semicontinuity, Stoilow factorization and principal maps

Kari Astala, Daniel Faraco, André Guerra +2

We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as…

math.AP2023

The local Burkholder functional, quasiconvexity and Geometric Function Theory

Kari Astala, Daniel Faraco, André Guerra +2

We show that the local Burkholder functional $B_{K}$ is quasiconvex. In the limit of $p$ going to 2 we find a class of non-polyconvex functionals which are quasiconvex on th…

math.CV2023

Extension of planar Hölder homeomorphisms

Stanislav Hencl, Aleksis Koski

Let $α$ \in (0; 1). We show that any $α$ -Hölder homeomorphism from the unit circle in the plane to the plane can be extended to an $α$ -Hölder homeomorphism from the whole unit disc…

math.CV2022

Bi-Sobolev extensions

Aleksis Koski, Jani Onninen

We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal varian…

math.CA2021

Sobolev homeomorphic extensions from two to three dimensions

Stanislav Hencl, Aleksis Koski, Jani Onninen

We study the basic question of characterizing which boundary homeomorphisms of the unit sphere can be extended to a Sobolev homeomorphism of the interior in 3D space. While the pla…

math.AP2021

Analytic characterization of monotone Hopf-harmonics

Ilmari Kangasniemi, Aleksis Koski, Jani Onninen

We study solutions of the inner-variational equation associated with the Dirichlet energy in the plane, given homeomorphic Sobolev boundary data. We prove that such a solution is m…

math.CV2020

The Sobolev Jordan-Schonflies Problem

Aleksis Koski, Jani Onninen

We consider the planar unit disk $D$ as the reference configuration and a Jordan domain $Y$ as the deformed configuration, and study the problem of extending a give…

math.CV2020

Sobolev homeomorphic extensions onto John domains

Pekka Koskela, Aleksis Koski, Jani Onninen

Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general…

math.CV2019★ 4 cited

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…

math.CV2019

Radially symmetry of minimizers to the weighted Dirichlet energy

Aleksis Koski, Jani Onninen

We consider the problem of minimizing the weighted Dirichlet energy between homeomorphisms of planar annuli. A known challenge lies in the case when the weight $λ$ depends on the i…

math.CV2018

Sobolev homeomorphic extensions

Aleksis Koski, Jani Onninen

Let $X$ and $Y$ be $ℓ$ -connected Jordan domains, $ℓ \in N$ , with rectifiable boundaries in the complex plane. We prove that any boundary homeomorphism…

math.AP2018

The Radó-Kneser-Choquet theorem for $p$ -harmonic mappings between Riemannian surfaces

Tomasz Adamowicz, Jarmo Jääskeläinen, Aleksis Koski

In the planar setting the Radó-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that…

math.CV2017★ 9 cited

Radial symmetry of p-harmonic minimizers

Aleksis Koski, Jani Onninen

"It is still not known if the radial cavitating minimizers obtained by Ball [J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R.…

math.CV2015★ 14 cited

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…

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

Characterizing Sobolev Homeomorphic Extensions via Internal Distances

Lower semicontinuity, Stoilow factorization and principal maps

The local Burkholder functional, quasiconvexity and Geometric Function Theory

Extension of planar Hölder homeomorphisms

Bi-Sobolev extensions

Sobolev homeomorphic extensions from two to three dimensions

Analytic characterization of monotone Hopf-harmonics

The Sobolev Jordan-Schonflies Problem

Sobolev homeomorphic extensions onto John domains

Improved Hölder regularity for strongly elliptic PDEs

Radially symmetry of minimizers to the weighted Dirichlet energy

Sobolev homeomorphic extensions

The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces

Radial symmetry of p-harmonic minimizers

Nonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian

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

The Radó-Kneser-Choquet theorem for $p$ -harmonic mappings between Riemannian surfaces