141 citations · 696 across the 45 of their papers we have counts for
51 papers
Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
Jean Dolbeault, Maria J. Esteban, Alessio Figalli +2
We prove a sharp quantitative version for the stability of the Sobolev inequality with explicit constants. Moreover, the constants have the correct behavior in the limit of large d…
On the eigenvalues of operators with gaps. Application to Dirac operators
Jean Dolbeault, Maria J. Esteban, Eric Séré
This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem…
Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators
Jean Dolbeault, Maria J. Esteban, Eric Séré
We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting…
Which nuclear shape generates the strongest attraction on a relativistic electron? An open problem in relativistic quantum mechanics
Maria J. Esteban, Mathieu Lewin, Eric Séré
In this article we formulate several conjectures concerning the lowest eigenvalue of a Dirac operator with an external electrostatic potential. The latter describes a relativistic…
Hardy-Littlewood-Sobolev and related inequalities: stability
Jean Dolbeault, Maria J. Esteban
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute…
Gagliardo-Nirenberg-Sobolev inequalities on planar graphs
Maria J. Esteban
In this paper we study a family of interpolation Gagliardo-Nirenberg-Sololev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities…