2 citations · 7 across the 10 of their papers we have counts for
5 papers · 1 filter
Hardy-Sobolev interpolation inequalities
Charlotte Dietze, Phan Thành Nam
We derive a family of interpolation estimates which improve Hardy's inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in t…
Isoperimetric inequalities for inner parallel curves
Charlotte Dietze, Ayman Kachmar, Vladimir Lotoreichik
We prove weighted isoperimetric inequalities for smooth, bounded, and simply connected domains. More precisely, we show that the moment of inertia of inner parallel curves for doma…
Weyl's law for Neumann Schrödinger operators on Hölder domains
Charlotte Dietze
We review recent results on the semiclassical behaviour of Schrödinger operators with Neumann boundary conditions. In this setting, the validity of Weyl's law requires additional c…
Focusing dynamics of 2D Bose gases in the instability regime
Lea Boßmann, Charlotte Dietze, Phan Thành Nam
We consider the dynamics of a 2D Bose gas with an interaction potential of the form for . The interaction may be chosen to be negative and large…
Semiclassical estimates for Schrödinger operators with Neumann boundary conditions on Hölder domains
Charlotte Dietze
We prove a universal bound for the number of negative eigenvalues of Schrödinger operators with Neumann boundary conditions on bounded Hölder domains, under suitable assumptions on…