11 papers
Moduli of the Sourceless Framed Beltrami-Vekua Normal Form
Daniel Alayón-Solarz
We study the moduli of sourceless framed Beltrami-Vekua equations under recombinations of the unknown, scalings, and orientation-preserving changes of variables. On every bounded s…
The Pseudo-Analytic Charge
Daniel Alayón-Solarz
The framed Beltrami--Vekua equation , with and $|Φ|>|…
The Framed Beltrami-Vekua Normal Form and its Pseudo-Analytic Mass
Daniel Alayón-Solarz
We normalize a first-order real planar elliptic system, by pointwise algebra, to a framed Beltrami-Vekua equation $Φ(w_{\bar z} - μw_z) + Ψ(\overline{w_z} - μ\,\overline{w_{\bar z}…
The complex form of Vekua's characteristic factor: a derivation, and two sign corrections in §7 of Generalized Analytic Functions
Daniel Alayón-Solarz
In \S7 of \emph{Generalized Analytic Functions} \cite{vekua}, the reduction of a first-order elliptic system to canonical form proceeds through a factor of the characteristic equat…
The Absorption Theorem for the Beltrami-Vekua Normal Form
Daniel Alayón-Solarz
The Beltrami-Vekua normal form assigns to every smooth first-order real planar elliptic system a complex equation by an…
The Pseudo-Analytic Mass of a Beltrami-Vekua Equation
Daniel Alayón-Solarz
Every smooth first-order real planar elliptic system admits a universal complex form , which we call the Beltr…
Arithmetic Uniformization of Rigid Elliptic Structures: From Rigid to Standard Vekua without the Beltrami Equation
Daniel Alayón-Solarz
For the rigid subclass of variable elliptic structures -- characterized equivalently by the inviscid Burgers law or the self-dilatation -- we show th…
The Burgers Transform: From Holomorphic Functions to Rigid Elliptic Structures
Daniel Alayón-Solarz
We introduce the Burgers transform , a nonlinear bijection between holomorphic functions and rigid variable elliptic structures on the plane…
A Degenerate Elliptic System Solvable by Transport: A Cautionary Example
Daniel Alayón-Solarz
We exhibit a one-parameter family of first-order real elliptic systems on the plane whose ellipticity constant degenerates to zero as , with condition number …
Variable Elliptic Structures on the Plane: Transport Dynamics, Rigidity, and Function Theory
Daniel Alayón-Solarz
We develop a theory of variable elliptic structures on planar domains, in which the imaginary unit is a moving generator of a rank-two real algebra bundle defined by a smo…
A note on elliptic first order systems in the plane and the Vekua Equation with structure polynomial
D. Alayón-Solarz
This note deals with the following problem: under which conditions can elliptic first order systems in the plane be complex-rewritten as a parameter-depending Vekua-type equation?