42 citations · 123 across the 17 of their papers we have counts for
25 papers
Sharp weighted log-Sobolev inequalities: characterization of equality cases and applications
Zoltán M. Balogh, Sebastiano Don, Alexandru Kristály
By using optimal mass transport theory, we provide a direct proof to the sharp -log-Sobolev inequality involving a log-concave homogeneous weight on an open convex…
On the geometry of irreversible metric-measure spaces: Convergence, Stability and Analytic aspects
Alexandru Kristály, Wei Zhao
The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact s…
Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature
Zoltán M. Balogh, Alexandru Kristály
By using optimal mass transport theory we prove a sharp isoperimetric inequality in metric measure spaces assuming an asymptotic volume growth at infinity. Our res…
Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups
Csaba Farkas, Alexandru Kristály, Ágnes Mester
Given a complete non-compact Riemannian manifold with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries of th…
Sobolev inequalities with jointly concave weights on convex cones
Zoltán M. Balogh, Cristian E. Gutiérrez, Alexandru Kristály
Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form \[\left(\int_E |u(x)|^q\,ω(x) \,dx\right)^{1/q}\leq K_0\,\left(\int_E |\nabla u(x)|^p\,σ(…
Differential inclusions involving oscillatory terms
Alexandru Kristály, Ildikó I. Mezei, Károly Szilák
Motivated by mechanical problems where external forces are non-smooth, we consider the differential inclusion problem \[ \begin{cases} -Δu(x)\in \partial F(u(x))+λ\partial G(u(x))\…
Fundamental tones of clamped plates in nonpositively curved spaces
Alexandru Kristály
We study Lord Rayleigh's problem for clamped plates on an arbitrary -dimensional Cartan-Hadamard manifold with sectional curvature for…
Topological rigidity of compact manifolds supporting Sobolev-type inequalities
Csaba Farkas, Alexandru Kristály, Ágnes Mester
Let be an -dimensional compact Riemannian manifold with Ric. If supports an AB-type critical Sobolev inequality with Sobolev con…
Interpolation between Brezis-Vázquez and Poincaré inequalities on nonnegatively curved spaces: sharpness and rigidities
Alexandru Kristály, Anikó Szakál
This paper is devoted to investigate an interpolation inequality between the Brezis-Vázquez and Poincaré inequalities (shortly, BPV inequality) on nonnegatively curved spaces. As a…
Sharp uncertainty principles on general Finsler manifolds
Libing Huang, Alexandru Kristály, Wei Zhao
The paper is devoted to sharp uncertainty principles (Heisenberg-Pauli-Weyl, Caffarelli-Kohn-Nirenberg and Hardy inequalities) on forward complete Finsler manifolds endowed with an…
Energy properties of critical Kirchhoff problems with applications
Francesca Faraci, Csaba Farkas, Alexandru Kristály
In this paper we fully characterize the sequentially weakly lower semicontinuity of the parameter-depending energy functional associated with the critical Kirchhoff problem. We als…
New features of the first eigenvalue on negatively curved spaces
Alexandru Kristály
The paper is devoted to the study of fine properties of the first eigenvalue on negatively curved spaces. First, depending on the parity of the space dimension, we provide asymptot…
Equality in Borell-Brascamp-Lieb inequalities on curved spaces
Zoltán M. Balogh, Alexandru Kristály
By using optimal mass transportation and a quantitative Hölder inequality, we provide estimates for the Borell-Brascamp-Lieb deficit on complete Riemannian manifolds. Accordingly,…
Jacobian determinant inequality on corank 1 Carnot groups with applications
Zoltán M. Balogh, Alexandru Kristály, Kinga Sipos
We establish a weighted pointwise Jacobian determinant inequality on corank 1 Carnot groups related to optimal mass transportation akin to the work of Cordero-Erausquin, McCann and…
Multipolar Hardy inequalities on Riemannian manifolds
Francesca Faraci, Csaba Farkas, Alexandru Kristály
We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [I…
Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature
Ezequiel Barbosa, Alexandru Kristály
Let be an dimensional complete open Riemannian manifold with nonnegative Ricci curvature verifying , where is the Laplace-Beltrami operator…
Metric projections versus non-positive curvature
Alexandru Kristály, Dušan Repovš
In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In pa…
Nash-type equilibria on Riemannian manifolds: a variational approach
Alexandru Kristály
Motivated by Nash equilibrium problems on 'curved' strategy sets, the concept of Nash-Stampacchia equilibrium points is introduced via variational inequalities on Riemannian manifo…
Multiple solutions for a Neumann system involving subquadratic nonlinearities
Alexandru Kristály, Dušan Repovš
In this paper we consider the model semilinear Neumann system $$\left\{ \begin{array}{lll} -Δu+a(x)u=λc(x) F_u(u,v)& {\rm in} & Ω,\\ -Δv+b(x)v=λc(x) F_v(u,v)& {\rm in} & Ω,\\ \frac…
On the Schrödinger-Maxwell system involving sublinear terms
Alexandru Kristály, Dušan Repovš
In this paper we study the coupled Schrödinger-Maxwell system $$\left\{ \begin{array}{lll} -\triangle u+u +ϕu=λα(x) f(u)& {\rm in} & \mathbb R^3,\\ -\triangle ϕ=u^2 & {\rm in} & \m…
Schrödinger-Maxwell systems on Hadamard manifolds
Csaba Farkas, Alexandru Kristály
In this paper we study nonlinear Schrödinger-Maxwell systems on dimensional Hadamard manifolds, The main difficulty resides in the lack of compactness of such…
New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case
Alexandru Kristály
In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement argum…
Elliptic problems on the ball endowed with Funk-type metrics
Alexandru Kristály, Imre J. Rudas
We study Sobolev spaces on the dimensional unit ball endowed with a parameter-depending Finsler metric , which interpolates between the Klein metric…
Quantitative Rellich Inequalities on Finsler-Hadamard Manifolds
Alexandru Kristály, Dušan Repovš
In this paper we are dealing with quantitative Rellich inequalities on Finsler-Hadamard manifolds where the remainder terms are expressed by means of the flag curvature. By explori…