Existence of solutions to a multidimensional analog of the Beltrami equation
type: Item
instance of: scholarly article
title: Existence of solutions to a multidimensional analog of the Beltrami equation
zbMATH Open document ID: 0695.35137
DOI: 10.1007/BF01054219
author: I. V. Zhuravlev
published in: Siberian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let \(U\subset C^ n\), \(\mu\) : \(U\to\) a set of complex \(n\times n\) matrices with measurable elements \(\mu_{kj}(z)\) \((k,j=1,...,n)\), belonging to the space \(L^{\infty}(U)\). In the paper for the following multidimensional analog of Beltrami equation: \[ (*)\quad {\bar \partial}_ kf(z)=\sum^{n}_{j=1}\partial_ jf(z)\mu_{jk}(z)\quad (k=1,...,n), \] where f: \(U\to C\) is a solution of (*) with general (in the Sobolev sense) derivatives \({\bar \partial}_ kf\), \(\partial_ kf\) \((k=1,...,n)\), a theorem on existence and uniqueness of the solution of the equation (*) is proved.
Mathematics Subject Classification ID: 35N10
Mathematics Subject Classification ID: 35F05
zbMATH DE Number: 4138376
zbMATH Keywords: multidimensional
zbMATH Keywords: Beltrami equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: Q3268429
cites work: Complex analytic coordinates in almost complex manifolds
cites work: Some integration problems in almost-complex and complex manifolds
cites work: Harmonic integrals on strongly pseudo-convex manifolds. I
cites work: Q4748438
cites work: Q3889369
cites work: Q5607391
full work available at URL: https://doi.org/10.1007/bf01054219
OpenAlex ID: W2013354980
description: scientific article; zbMATH DE number 4138376