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20142025

most citedNew bounds on the condition number of the Hessian of the preconditioned variational data assimilation problem

10 citations

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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.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.AP2014★ 1 cited

Remarks on the validity on the maximum principle for the $\infty$ -Laplacian

Nikos Katzourakis, Juan Manfredi

In this note we give three counter-examples which show that the Maximum Principle generally fails for classical solutions of a system and a single equation related to the $\infty$ -…

math.AP2014★ 1 cited

On the Dirichlet Problem for Fully Nonlinear Elliptic Hessian Systems

Nikos Katzourakis

We consider the problem of existence and uniqueness of strong solutions $u : Ω \subset R^{n} ⟶ R^{N}$ in $(H^{2} \cap H_{0}^{1}) (Ω)^{N}$ to the problem \[\labe…

On the minimisation of the Peak-to-average ratio

On the numerical approximation of vectorial absolute minimisers in L∞

Remarks on the validity on the maximum principle for the ∞-Laplacian

On the Dirichlet Problem for Fully Nonlinear Elliptic Hessian Systems

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

Remarks on the validity on the maximum principle for the $\infty$ -Laplacian