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

In this paper we utilise new methods of Calculus of Variations in L ∞ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet data on a domain. One of the advantages over the classical Tykhonov regularisation in L 2 is that the approximated solution of the PDE is uniformly close to the noisy measurements taken on a compact subset of the domain

Inverse optical tomography through PDE constrained optimisation in L∞

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 no side effects for humans, as it uses non-ionising red and infrared light. Mathematically, FOT can be modelled as an inverse parameter identification problem, associated with a coupled elliptic system with Robin boundary conditions. Herein we utilise novel methods of Calculus of Variations in L∞ to lay the mathematical foundations of FOT which we pose as a PDE-constrained minimisation problem in Lp and L∞

Gamma-convergence of power-law functionals, variational principles in L-infinity, and application

Two Gamma-convergence results for a general class of power-law functionals are obtained in the setting of A-quasiconvexity. New variational principles in L^{infty} are introduced, allowing for the description of the yield set in the context of a simplified model of polycrystal plasticity. A number of highly degenerate nonlinear partial differential equations arise as Aronsson equations associated with these variational principles

A perturbation result for a double eigenvalue hemivariational inequality with constraints and applications

Abstract. In this paper we prove a perturbation result for a new type of eigenvalue problem intro-duced by D. Motreanu and P.D. Panagiotopoulos (1998). The perturbation is made in the nonsmooth and nonconvex term of a double eigenvalue problem on a spherlike type manifold considered in ‘Multiple solutions for a double eigenvalue hemivariational inequality on a spherelike type manifold’ (to appear in Nonlinear Analysis). For our aim we use some techniques related to the Lusternik-Schnirelman theory (including Krasnoselski’s genus) and results proved by J.N. Corvellec et al