Bilge Köksal | Searcharxiv

arXiv2026

Idealistic equivalence relations and the Lusin derivative

We give a proof, that does not rely on analytic determinacy, of the existence of an idealistic analytic equivalence relation with Borel classes that is not classwise Borel isomorphic to an orbit equivalence relation. This result answers a question of Becker, and Calderoni and Motto Ros. Our proof proceeds through an analysis of Borel complexity of certain sets of countable rooted trees defined via the notion of the Lusin derivative.

math.LO↗

arXiv2022

The interior-boundary Strichartz estimate for the Schrödinger equation on the half line revisited

It was shown by the second author in (CPAA, 2019) for the biharmonic Schrödinger equation and most recently by Himonas and Mantzavinos (Nonlinearity, 2020) for 2D Schrödinger equation that Fokas method based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interior-boundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with Dirichlet/Neumann boundary conditions.

math.AP↗