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

Variational dimension reduction in nonlinear elasticity: a Young measure approach

Starting form 3D elasticity, we deduce the variational limit of the string and of the membrane on the space of one and two-dimensional gradient Young measures, respectively. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account in the string model. The rate at which the energy density blows up characterizes the effective domain of the limit energy. The limit problem uniquely determines the energy density of the thin structure. © 2008 Springer Science+Business Media B.V