19 citations · 116 across the 42 of their papers we have counts for
7 papers · 1 filter
On the numerical approximation of vectorial absolute minimisers in
Nikos Katzourakis, Tristan Pryer
Let be an open set. We consider the supremal functional \[ \tag{1} \label{1} \ \ \ \ \ \ \mathrm{E}_\infty (u,\mathcal{O})\, :=\, \| \mathrm D u \|_{L^\infty( \mathcal{O} )}, \…
Inverse optical tomography through PDE constrained optimisation in
Nikos Katzourakis
Fluorescent Optical Tomography (FOT) is a new bio-medical imaging method with wider industrial applications. It is currently intensely researched since it is very precise and with…
A minimisation problem in with PDE and unilateral constraints
Nikos Katzourakis
We study the minimisation of a cost functional which measures the misfit on the boundary of a domain between a component of the solution to a certain parametric elliptic PDE system…
On a vector-valued generalisation of viscosity solutions for general PDE systems
Nikos Katzourakis
We propose a theory of non-differentiable solutions which applies to fully nonlinear PDE systems and extends the theory of viscosity solutions of Crandall-Ishii-Lions to the vector…
Vectorial variational principles in and their characterisation through PDE systems
Birzhan Ayanbayev, Nikos Katzourakis
We discuss two distinct minimality principles for general supremal first order functionals for maps and characterise them through solvability of associated second order PDE systems…
An regularisation strategy to the inverse source identification problem for elliptic equations
Nikos Katzourakis
In this paper we utilise new methods of Calculus of Variations in to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a no…
Counterexamples in Calculus of Variations in through the vectorial Eikonal equation
Nikos Katzourakis, Giles Shaw
We show that for any regular bounded domain , , there exist infinitely many global diffeomorphisms equal to the identity on which solve…