Jarosław Mederski

activity

20132026

most citedNormalized ground states of the nonlinear Schrödinger equation with at least mass critical growth

103 citations · 301 across the 31 of their papers we have counts for

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Showing 2026 · math.APShow all

5 papers · 2 filters

math.AP2026

Critical curl extremals and the hyperbolic plane

Jarosław Mederski

We study the critical Sobolev-curl quotient on $R^{3}$ at the conformally invariant exponent $p = 3/2$ . Its sharp constant and optimizers were posed as open problems in the li…

math.AP2026

Global well-posedness and orbital stability of the Gross--Pitaevskii branch in a coupled defocusing Schrödinger system

Michał Kowalczyk, Jarosław Mederski, Isidora Miranda

We consider a one-dimensional coupled defocusing Schrödinger system with a nonzero background in its first component and finite mass in its second component. We prove global well-p…

math.AP2026

On a critical curl-curl system of Lane-Emden type

Ioannis Arkoudis, Jarosław Mederski, Andrzej Szulkin

We study the system $\nabla \times \nabla \times u = ∣ v ∣^{q - 2} v$ , $\nabla \times \nabla \times v = ∣ u ∣^{p - 2} u$ of Lane-Emden type in $R^{3}$ , with exponents $p, q > 3$ on the critical…

math.AP2026

Explicit counterexamples to Frank-Loss optimizer conjectures for critical Dirac and vector Sobolev inequalities

Bartosz Bieganowski, Jarosław Mederski

Frank and Loss proposed critical Sobolev inequalities for the Dirac operator and for vector fields. They conjectured optimality of their spinorial family and wrote that it is conce…

math.AP2026

Ground state solutions to Born-Infeld-Choquard problem

Jarosław Mederski, Xiangjian Zeng

In this paper, we investigate the existence and qualitative properties of ground state solutions for the nonlocal Born-Infeld-Choquard problem \begin{equation*} \begin{cases} -{\rm…