19 citations · 116 across the 42 of their papers we have counts for
8 papers · 2 filters
On the Numerical Approximation of -Harmonic Mappings
Nikos Katzourakis, Tristan Pryer
Given a map , the -Laplacian is the system \[ \label{1} Δ_\infty u \, :=\, \Big(\text{D}u \otimes \text{D}u + |\te…
On the Well-Posedness of Global Fully Nonlinear First Order Elliptic Systems
Hussien Abugirda, Nikos Katzourakis
In the very recent paper [K1], the second author proved that for any , the fully nonlinear first order system is we…
A New Characterisation of -Harmonic and -Harmonic Maps via Affine Variations in
Nikos Katzourakis
Let be a smooth map and . The -Laplacian is the PDE system \[ \tag{1} \label{1} Δ_\infty u \,…
Mollification of -solutions to Fully Nonlinear PDE Systems
Nikos Katzourakis
In a recent paper (arXiv:1501.06164) the author has introduced a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows the interp…
Weak versus -solutions to linear hyperbolic first order systems with constant coefficients
Nikos Katzourakis
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coeffici…
On Linear Degenerate Elliptic PDE Systems with Constant Coefficients
Nikos Katzourakis
Let be a symmetric convex quadratic form on and a bounded convex domain. We consider the problem of existence of solutions $u…
Absolutely Minimising Generalised Solutions to the Equations of Vectorial Calculus of Variations in
Nikos Katzourakis
Consider the supremal functional \[ \tag{1} \label{1} E_\infty(u,A) \,:=\, \|L(\cdot,u,D u)\|_{L^\infty(A)},\quad A\subseteq Ω, \] applied to maps $u:Ω\subseteq \mat…
Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness Theorems
Nikos Katzourakis
We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypas…