Homeomorphic Solutions to Reduced Beltrami Equations (2008)
Astala, Kari, Jääskeläinen, Jarmo
This paper studies differential expressions related to linear families of quasiconformal mappings, and generalizes a result of Alessandrini and Nesi arXiv:0707.0727 to a global setting. We use...
Optimal regularity for planar mappings of finite distortion (2008)
Astala, Kari, Gill, James, Rohde, Steffen, Saksman, Eero
Let $f:\Omega\to\IR^2$ be a mapping of finite distortion, where $\Omega\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies $e^{K(\cdot, f)}\in L^p_{loc}(\Omega)$ for some $p>0.$ We...
On Semifredholm Operators and the Calkin Algebra (2006)
Astala, Kari, Tylli, Hans-Olav
We study the algebraic properties of the canonical images π(Φ+(E)) and π(Φ−(E)) of semiFredholm operators in the Calkin algebra C(E). The properties depend strongly on the underlying...
Astala, Kari, Clop, Albert, Mateu, Joan, Orobitg, Joan, Uriarte-Tuero, Ignacio
The classical Painlev\'e theorem tells that sets of zero length are removable for bounded analytic functions, while (some) sets of positive length are not. For general $K$-quasiregular mappings in...
Calderón's inverse conductivity problem in the plane (2006)
Astala, Kari, Päivärinta, Lassi
We show that the Dirichlet to Neumann map for the equation $ \nabla\cdot\sigma\nabla u = 0$ in a two-dimensional domain uniquely determines the bounded measurable conductivity $ \sigma$. This gives a...
A boundary integral equation for Calderón's inverse conductivity problem (2006)
Astala, Kari, Päivärinta, Lassi
Towards a constructive method to determine an L1-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a...
Calderón's inverse conductivity problem in the plane (2006)
Astala, Kari, Päivärinta, Lassi
We show that the Dirichlet to Neumann map for the equation ¿Þ¿E¿Ð¿Þu = 0 in a two-dimensional domain uniquely determines the bounded measurable conductivity ¿Ð. This gives a positive answer...
Extremal mappings of finite distortion (2005)
Astala, Kari, Iwaniec, T., Martin, G. J., Onninen, J.
The theory of mappings of finite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting where...
Calderon's inverse problem for anisotropic conductivity in the plane (2004)
Astala, Kari, Lassas, Matti, Paivarinta, Lassi
We study inverse conductivity problem for an anisotropic conductivity in $L^\infty$ in bounded and unbounded domains. Also, we give applications of the results in the case when Dirichlet-to-Neumann...
Convex integration and the Lp theory of elliptic equations (2004)
Astala, Kari, Faraco, Daniel, Székelyhidi, László
We consider elliptic partial differential equations and provide a method constructing solutions with critical integrability properties. We illustrate the technique by studying isotropic equations and...
Beltrami operators in the plane (2001)
Astala, Kari, Iwaniec, Tadeusz, Saksman, Eero
We determine optimal Lp-properties for the solutions of the general nonlinear elliptic system in the plane of the form f \overline{z} =H(z, fz), h∈ Lp(C), where H is a measurable function...
Calderón's Problem for Lipschitz Classes and the Dimension of Quasicircles. (1988)
In the last years the mapping properties of the Cauchy integral CGf(z) = 1/(2pi) ?G [f(?) / ? - z] d? have been widely studied. The most important question in this area was Calderón's problem, to...