141 citations · 781 across the 77 of their papers we have counts for
9 papers · 2 filters
Improved interpolation inequalities on the sphere
Jean Dolbeault, Maria J. Esteban, Michal Kowalczyk +1
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we…
Bifurcation diagrams and multiplicity for nonlocal elliptic equations modeling gravitating systems based on Fermi-Dirac statistics
Jean Dolbeault, Robert Stanczy
This paper is devoted to multiplicity results of solutions to nonlocal elliptic equations modeling gravitating systems. By considering the case of Fermi-Dirac statistics as a singu…
One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: Remarks on duality and flows
Jean Dolbeault, Maria J. Esteban, Ari Laptev +1
This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals…
Existence of steady states for the Maxwell-Schrödinger-Poisson system: exploring the applicability of the concentration-compactness principle
Isabelle Catto, Jean Dolbeault, Óscar Sánchez +1
This paper is intended to review recent results and open problems concerning the existence of steady states to the Maxwell-Schrödinger system. A combination of tools, proofs and re…
Stationary solutions of Keller-Segel type crowd motion and herding models: multiplicity and dynamical stability
Jean Dolbeault, Peter Markowich, Gaspard Jankowiak
In this paper we study two models for crowd motion and herding. Each of the models is of Keller-Segel type and involves two parabolic equations, one for the evolution of the densit…
Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations
Jean Dolbeault, Maria J. Esteban
In this paper we study the bifurcation of branches of non-symmetric solutions from the symmetric branch of solutions to the Euler-Lagrange equations satisfied by optimal functions…