Nikos Katzourakis

activity

20072026

most citedAbsolutely Minimising Generalised Solutions to the Equations of Vectorial Calculus of Variations in

L^{\infty}

19 citations · 116 across the 42 of their papers we have counts for

collaborators

51 papers

math.AP2026

Semi-differentiability of generalised $L^{\infty}$ envelopes with applications to supremal functionals

Nikos Katzourakis

J. Danskin proved in 1966 that the envelope of a family of continuous functions $F : R^{n} \times K ⟶ R$ , parameterised by the points of…

math.AP2026

An introduction to the vectorial Calculus of Variations in $L^{\infty}$ AND Aronsson PDE systems

Hussien Abugirda, Nikos Katzourakis

In this expository article, which is partially based on the lecture notes of a short course delivered by the second appearing author, we introduce the subfield of the Calculus of V…

math.AP2026

Generalised higher order vectorial $\infty$ -eigenvalue problems

William Chang, Nikos Katzourakis

We study the problem of minimising the $L^{\infty}$ norm of a function of the $k$ -th derivative over a class of maps, subject to a constraint involving the $L^{\infty}$ norm of a funct…

math.AP2026

Energy maximum principle for vectorial higher order absolute minimisers in $L^{\infty}$ and $L^{p}$

Simone Carano, Nikos Katzourakis, Roger Moser

We show that vectorial absolute minimisers of general $k$ -th order supremal functionals in $W^{k, \infty} (Ω, R^{N})$ satisfy a maximum principle of the form $$ \max_{\overline…

math.AP2026

On General Linear Degenerate Elliptic PDE Systems

Nikos Katzourakis, Frederick Temple

Let $Ω ⋐ R^{n}$ be a strictly convex bounded domain. Suppose $A : R^{N n} ⟶ R^{N n}$ , $\mathbf{B}: \mathbb{R}^{Nn} \longrightar…

math.AP2025

Existence, uniqueness and characterisation of vector-valued absolute minimisers for a second order $L^{\infty}$ -variational problem

Simone Carano, Nikos Katzourakis, Roger Moser

We study a vectorial $L^{\infty}$ -variational problem of second order, where the supremal functional depends on the vector function $u$ through a linear elliptic operator in divergen…

math.AP2025

On the minimisation of the Peak-to-average ratio

Nikos Katzourakis

Let $Ω ⋐ R^{n}$ and a continuous function $H$ be given, where $n, k, N \in N$ . For $p \in [1, \infty]$ , we consider the functional \[ \mathrm E_p(u) := \big\…

math.AP2025

On Second-Order $L^{\infty}$ Variational Problems with Lower-Order Terms

Ben Dutton, Nikos Katzourakis

In this paper we study $2$ nd order $L^{\infty}$ variational problems, through seeking to minimise a supremal functional involving the Hessian of admissible functions as well as lower…

math.AP2024

Existence, uniqueness and characterisation of local minimisers in higher order Calculus of Variations in $L^{\infty}$

Nikos Katzourakis, Roger Moser

We study variational problems for second order supremal functionals $F_{\infty} (u) = ∥ F (\cdot, u, D u, A : D^{2} u) ∥_{L^{\infty} (Ω)}$ , where $F$ …

math.AP2024★ 3 cited

Minimisers of supremal functionals and mass-minimising 1-currents

Nikos Katzourakis, Roger Moser

We study vector-valued functions that minimise the $L^{\infty}$ -norm of their derivatives for prescribed boundary data. We construct a vector-valued, mass minimising $1$ -current (i.e…

math.AP2023★ 5 cited

Variational problems in $L^{\infty}$ involving semilinear second order differential operators

Nikos Katzourakis, Roger Moser

For an elliptic, semilinear differential operator of the form $S (u) = A : D^{2} u + b (x, u, D u)$ , consider the functional $E_{\infty} (u) = ess sup_{Ω} ∣ S (u) ∣$ . We st…

math.AP2023

Generalised second order vectorial $\infty$ -eigenvalue problems

Ed Clark, Nikos Katzourakis

We consider the problem of minimising the $L^{\infty}$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^{\infty}$ norm of a functio…

math.AP2022★ 1 cited

On isosupremic vectorial minimisation problems in $L^{\infty}$ with general nonlinear constraints

Ed Clark, Nikos Katzourakis

We study minimisation problems in $L^{\infty}$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another…

math.AP2021

Vectorial variational problems in $L^{\infty}$ constrained by the Navier-Stokes equations

Ed Clark, Nikos Katzourakis, Boris Muha

We study a minimisation problem in $L^{p}$ and $L^{\infty}$ for certain cost functionals, where the class of admissible mappings is constrained by the Navier-Stokes equations. Problems…

math.AP2021

Generalised vectorial $\infty$ -eigenvalue nonlinear problems for $L^{\infty}$ functionals

Nikos Katzourakis

Let $Ω ⋐ R^{n}$ , $f \in C^{1} (R^{N \times n})$ and $g \in C^{1} (R^{N})$ , where $N, n \in N$ . We study the minimisation problem of finding $u \in W^{1,\inf…

math.AP2020

On the inverse source identification problem in $L^{\infty}$ for fully nonlinear elliptic PDE

Birzhan Ayanbayev, Nikos Katzourakis

In this paper we generalise the results proved in [N. Katzourakis, An $L^{\infty}$ regularisation strategy to the inverse source identification problem for elliptic equations, SIAM J…

math.AP2018

On the numerical approximation of vectorial absolute minimisers in $L^{\infty}$

Nikos Katzourakis, Tristan Pryer

Let $Ω$ 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} )}, \…

math.AP2018★ 1 cited

Inverse optical tomography through PDE constrained optimisation in $L^{\infty}$

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…

math.AP2018

A minimisation problem in $L^{\infty}$ 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…

math.AP2018

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…

math.AP2018

Vectorial variational principles in $L^{\infty}$ 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…

math.AP2018★ 1 cited

An $L^{\infty}$ 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 $L^{\infty}$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a no…

math.AP2018

Counterexamples in Calculus of Variations in $L^{\infty}$ through the vectorial Eikonal equation

Nikos Katzourakis, Giles Shaw

We show that for any regular bounded domain $Ω \subseteq R^{n}$ , $n = 2, 3$ , there exist infinitely many global diffeomorphisms equal to the identity on $\partial Ω$ which solve…

math.AP2017

Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian

Hussien Abugirda, Birzhan Ayanbayev, Nikos Katzourakis

In this paper we consider the PDE system of vanishing normal projection of the Laplacian for $C^{2}$ maps $u : R^{n} \supseteq Ω ⟶ R^{N}$ : \[ [\![\mathrm{D…

Semi-differentiability of generalised L∞ envelopes with applications to supremal functionals

An introduction to the vectorial Calculus of Variations in L∞ AND Aronsson PDE systems

Generalised higher order vectorial ∞-eigenvalue problems

Energy maximum principle for vectorial higher order absolute minimisers in L∞ and Lp

On General Linear Degenerate Elliptic PDE Systems

Existence, uniqueness and characterisation of vector-valued absolute minimisers for a second order L∞-variational problem

On the minimisation of the Peak-to-average ratio

On Second-Order L∞ Variational Problems with Lower-Order Terms

Existence, uniqueness and characterisation of local minimisers in higher order Calculus of Variations in L∞

Minimisers of supremal functionals and mass-minimising 1-currents

Variational problems in L∞ involving semilinear second order differential operators

Generalised second order vectorial ∞-eigenvalue problems

On isosupremic vectorial minimisation problems in L∞ with general nonlinear constraints

Vectorial variational problems in L∞ constrained by the Navier-Stokes equations

Generalised vectorial ∞-eigenvalue nonlinear problems for L∞ functionals

On the inverse source identification problem in L∞ for fully nonlinear elliptic PDE

On the numerical approximation of vectorial absolute minimisers in L∞

Inverse optical tomography through PDE constrained optimisation in L∞

A minimisation problem in L∞ with PDE and unilateral constraints

On a vector-valued generalisation of viscosity solutions for general PDE systems

Vectorial variational principles in L∞ and their characterisation through PDE systems

An L∞ regularisation strategy to the inverse source identification problem for elliptic equations

Counterexamples in Calculus of Variations in L∞ through the vectorial Eikonal equation

Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian

Semi-differentiability of generalised $L^{\infty}$ envelopes with applications to supremal functionals

An introduction to the vectorial Calculus of Variations in $L^{\infty}$ AND Aronsson PDE systems

Generalised higher order vectorial $\infty$ -eigenvalue problems

Energy maximum principle for vectorial higher order absolute minimisers in $L^{\infty}$ and $L^{p}$

Existence, uniqueness and characterisation of vector-valued absolute minimisers for a second order $L^{\infty}$ -variational problem

On Second-Order $L^{\infty}$ Variational Problems with Lower-Order Terms

Existence, uniqueness and characterisation of local minimisers in higher order Calculus of Variations in $L^{\infty}$

Variational problems in $L^{\infty}$ involving semilinear second order differential operators

Generalised second order vectorial $\infty$ -eigenvalue problems

On isosupremic vectorial minimisation problems in $L^{\infty}$ with general nonlinear constraints

Vectorial variational problems in $L^{\infty}$ constrained by the Navier-Stokes equations

Generalised vectorial $\infty$ -eigenvalue nonlinear problems for $L^{\infty}$ functionals

On the inverse source identification problem in $L^{\infty}$ for fully nonlinear elliptic PDE

On the numerical approximation of vectorial absolute minimisers in $L^{\infty}$

Inverse optical tomography through PDE constrained optimisation in $L^{\infty}$

A minimisation problem in $L^{\infty}$ with PDE and unilateral constraints

Vectorial variational principles in $L^{\infty}$ and their characterisation through PDE systems

An $L^{\infty}$ regularisation strategy to the inverse source identification problem for elliptic equations

Counterexamples in Calculus of Variations in $L^{\infty}$ through the vectorial Eikonal equation