# Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)

@inproceedings{Astala2009EllipticPD, title={Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)}, author={Kari Astala and Tadeusz Iwaniec and Gaven J. Martin}, year={2009} }

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account…

## 538 Citations

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To the theory of semilinear equations in the plane

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In two dimensions, we present a new approach to the study of the semilinear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is the divergence uniform elliptic operator with…