19 citations · 116 across the 42 of their papers we have counts for
6 papers · 1 filter
Remarks on the validity on the maximum principle for the -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 -…
Lecture notes on Viscosity Solutions for fully nonlinear 2nd order PDE and applications to Calculus of Variations in
Nikos Katzourakis
The purpose of these expository notes is to give a quick and elementary, yet rigorous, presentation of the rudiments of the theory of Viscosity Solutions for fully nonlinear 2nd or…
On the Dirichlet Problem for Fully Nonlinear Elliptic Hessian Systems
Nikos Katzourakis
We consider the problem of existence and uniqueness of strong solutions in to the problem \[\labe…
A review from the PDE viewpoint of Hamilton-Jacobi-Bellman Equations Arising in Optimal Control with Vectorial Cost
Nikos Katzourakis, Tristan Pryer
This paper is a review of results on Optimisation which are perhaps not so standard in the PDE realm. To this end, we consider the problem of deriving the PDEs associated to the op…
Existence and Uniqueness of Global Strong Solutions to Fully Nonlinear Second Order Elliptic Systems
Nikos Katzourakis
We consider the problem of existence and uniqueness of strong a.e. solutions to the fully nonlinear PDE system \[\label{1} \tag{1} F(…
Existence and Uniqueness of Global Solutions to Fully Nonlinear First Order Elliptic Systems
Nikos Katzourakis
Let be a Caratheodory map. In this paper we consider the problem of existence and uniqueness of weakly dif…