6 papers
A topology-changing variational framework for the Einstein-Hilbert functional
Miltiadis Paschalis
Motivated by recent developments in the theory of gravitation, we revisit the idea of topological variations, originally introduced by Wheeler and Hawking, from a rigorous perspect…
Semilinear Schrödinger equations with Hardy potentials involving the distance to a boundary submanifold and gradient source nonlinearities
Konstantinos T. Gkikas, Miltiadis Paschalis
Let () be a bounded domain and be a compact submanifold of dimension . Denote the distance from by . In…
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…
Shape sensitivity of the Hardy constant involving the distance to a boundary submanifold
Miltiadis Paschalis
We investigate the continuity and differentiability of the Hardy constant with respect to perturbations of the domain in the case where the problem involves the distance from a bou…
Geometric Hardy inequalities via integration on flows
Miltiadis Paschalis
We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equip…
Finsler-Rellich inequalities involving the distance to the boundary
Gerassimos Barbatis, Miltiadis Paschalis
We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the…