22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Regularisation of certain non-linear problems in $L^{\infty}$

23 Sep 2021, 11:50
20m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

Speaker

Dr Lukas Pieronek (KIT)

Description

In many cases the parameters of interest in inverse problems arise as coefficients of PDE models for which $L^{\infty}$ is one of the most natural spaces. Despite its formal connection to the regular and regularisation-approved $L^p$-spaces, $L^{\infty}$ itself is non-smooth, non-reflexive and non-separable. Hence, standard Banach space methods generally fail and the need of discretisation in practice makes it even hopeless to aim for good reconstructions in the strong topology. In this talk we present a novel regularisation method which generates uniformly bounded iterates as approximate solutions to locally ill-posed equations and for which the regularisation property then holds with respect to weak-$\ast$ convergence. Numerical examples will complete our analysis.

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