Variational Integrals and Quasiregular Mappings

1993 ◽  
pp. 129-161
Author(s):  
Seppo Rickman
Keyword(s):  
Quasiregular Mappings ◽  
Variational Integrals

scholarly journals Hardy Spaces for Quasiregular Mappings and Composition Operators

2021 ◽  
Author(s):  
Tomasz Adamowicz ◽  
María J. González
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Quasiconformal Mappings ◽  
Carleson Measures ◽  
Quasiregular Mappings ◽  
Classical Setting ◽  
Appl Math ◽  
Analytic Mappings

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

scholarly journals On the internal approach to differential equations. 1. The involutiveness and standard basis

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Veronika Chrastinová ◽  
Václav Tryhuk
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Commutative Algebra ◽  
Geometrical Theory ◽  
Technical Tool ◽  
Full Generality ◽  
Dependent Variables ◽  
Variational Integrals ◽  
Independent Variable

AbstractThe article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are subject to arbitrary transformations of variables in the widest possible sense. In this preparatory Part 1, the involutivity and the related standard bases are investigated as a technical tool within the framework of commutative algebra. The particular case of ordinary differential equations is briefly mentioned in order to demonstrate the strength of this approach in the study of the structure, symmetries and constrained variational integrals under the simplifying condition of one independent variable. In full generality, these topics will be investigated in subsequent Parts of this article.

scholarly journals On the order of quasiregular mappings

1982 ◽  
Vol 7 ◽  
pp. 221-231 ◽  
Author(s):  
S. Rickman ◽  
M. Vuorinen
Keyword(s):  
Quasiregular Mappings
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