Date/heure
9 février 2024
11:00 - 12:00
Oratrice ou orateur
Badreddine Benhellal (Universität Oldenburg)
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
In this talk, we discuss the self-adjointness in $L^2$-setting of the operators acting as $-\mathrm{div}\cdot h\nabla$, with piecewise constant functions $h$ having a jump along a Lipschitz hypersurface $\Sigma$, without explicit assumptions on the sign of $h$. We establish a number of sufficient conditions for the selfadjointness of the operator with $H^{\frac{3}{2}}$-regularity in terms of the jump value and the regularity and geometric properties of $\Sigma$. An important intermediate step is a link with Fredholm properties of the NeumannPoincaré operator on $\Sigma$, which is new for the Lipschitz setting.
Based on joint work with Konstantin Pankrashkin.