M. Paschalis

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math.AP2024

Hardy inequalities and uncertainty principles in the presence of a black hole

Miltiadis Paschalis

In this paper we establish Hardy and Heisenberg uncertainty-type inequalities for the exterior of a Schwarzschild black hole. The weights that appear in both inequalities are tailo…

math.AP2024

Semilinear SchrÃ¶dinger equations with Hardy potentials involving the distance to a boundary submanifold and gradient source nonlinearities

Konstantinos T. Gkikas, Miltiadis Paschalis

Let $I^c ◯ \subset R^{N}$ ( $N \geq 3$ ) be a bounded $C^{2}$ domain and $I^£ \subset \partial I^c ◯$ be a compact $C^{2}$ submanifold of dimension $k$ . Denote the distance from $I^£$ by $d_{I^} £$ …