Distributional solutions of the Beltrami equation

A. L. Baisón; A. Clop; J. Orobitg

doi:10.1016/j.jmaa.2018.10.050

Distributional solutions of the Beltrami equation

A. L. Baisón, A. Clop, J. Orobitg

Research output: Contribution to journal › Article › Research

Abstract

© 2018 Elsevier Inc. We study the distributional solutions to the (generalized) Beltrami equation under Sobolev assumptions on the Beltrami coefficients. In this setting, we prove that these distributional solutions are true quasiregular maps and they are smoother than expected, that is, they have second order derivatives in Lloc1+ε, for some ε>0.

Original language	English
Pages (from-to)	1081-1094
Journal	Journal of Mathematical Analysis and Applications
Volume	470
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.10.050
Publication status	Published - 15 Feb 2019

Keywords

Beltrami operators
Beltrami's equation
Distributional solution
Quasiconformal mapping

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title = "Distributional solutions of the Beltrami equation",

abstract = "{\textcopyright} 2018 Elsevier Inc. We study the distributional solutions to the (generalized) Beltrami equation under Sobolev assumptions on the Beltrami coefficients. In this setting, we prove that these distributional solutions are true quasiregular maps and they are smoother than expected, that is, they have second order derivatives in Lloc1+ε, for some ε>0.",

keywords = "Beltrami operators, Beltrami's equation, Distributional solution, Quasiconformal mapping",

author = "Bais{\'o}n, {A. L.} and A. Clop and J. Orobitg",

year = "2019",

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doi = "10.1016/j.jmaa.2018.10.050",

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journal = "Journal of Mathematical Analysis and Applications",

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TY - JOUR

T1 - Distributional solutions of the Beltrami equation

AU - Baisón, A. L.

AU - Clop, A.

AU - Orobitg, J.

PY - 2019/2/15

Y1 - 2019/2/15

N2 - © 2018 Elsevier Inc. We study the distributional solutions to the (generalized) Beltrami equation under Sobolev assumptions on the Beltrami coefficients. In this setting, we prove that these distributional solutions are true quasiregular maps and they are smoother than expected, that is, they have second order derivatives in Lloc1+ε, for some ε>0.

AB - © 2018 Elsevier Inc. We study the distributional solutions to the (generalized) Beltrami equation under Sobolev assumptions on the Beltrami coefficients. In this setting, we prove that these distributional solutions are true quasiregular maps and they are smoother than expected, that is, they have second order derivatives in Lloc1+ε, for some ε>0.

KW - Beltrami operators

KW - Beltrami's equation

KW - Distributional solution

KW - Quasiconformal mapping

U2 - 10.1016/j.jmaa.2018.10.050

DO - 10.1016/j.jmaa.2018.10.050

M3 - Article

VL - 470

SP - 1081

EP - 1094

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -