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View article: Generalized Strichartz estimates for the massive Dirac equation with critical potentials
Generalized Strichartz estimates for the massive Dirac equation with critical potentials Open
In this paper we prove generalized Strichartz estimates for the massive Dirac equation in the case of two critical potential perturbations, namely the $2d$ Aharonov-Bohm magnetic potential and the $3d$ Coulomb potential. The proof makes us…
View article: Steady three-dimensional rotational flows: existence via Kato's approach to locally coercive problems
Steady three-dimensional rotational flows: existence via Kato's approach to locally coercive problems Open
Stationary flows of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb R^2$, periodic in the second and third variables, are considered. The flux and the Bernoulli function are prescribed at each…
View article: A local surjection theorem with continuous inverse in Banach spaces
A local surjection theorem with continuous inverse in Banach spaces Open
In this paper, we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives.
View article: A local surjection theorem with continuous inverse in Banach spaces
A local surjection theorem with continuous inverse in Banach spaces Open
In this paper we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives.
View article: Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac–Coulomb operators
Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac–Coulomb operators Open
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 of the Hilbert space and has a variational gap property ass…
View article: Exponential decay of the critical points in a discrete model of polyacetylene
Exponential decay of the critical points in a discrete model of polyacetylene Open
In this paper we consider stationary states of the SSH model for infinite polyacetylene chains that are homoclinic or heteroclinic connections between two-periodic dimerized states. We prove that such connections converge exponentially fas…
View article: Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications
Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications Open
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View article: Existence of minimizers for the Dirac-Fock model of crystals
Existence of minimizers for the Dirac-Fock model of crystals Open
Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and we are not aware of any mathematical result on a fully rela…
View article: Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators
Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators Open
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 of the Hilbert space and has a variational gap property ass…
View article: Dispersive Estimates for the Dirac–Coulomb Equation
Dispersive Estimates for the Dirac–Coulomb Equation Open
We review some recent results on the dispersive estimates for the massless Dirac–Coulomb equation in 3D.
View article: Dirac–Coulomb operators with general charge distribution I. Distinguished extension and min-max formulas
Dirac–Coulomb operators with general charge distribution I. Distinguished extension and min-max formulas Open
This paper is the first of a series where we study the spectral properties of Dirac operators with the Coulomb potential generated by any finite signed charge distribution . We show here that the operator has a unique distinguished self-ad…
View article: Convergence analysis of adaptive DIIS algorithms with application to electronic ground state calculations
Convergence analysis of adaptive DIIS algorithms with application to electronic ground state calculations Open
This paper deals with a general class of algorithms for the solution of fixed-point problems that we refer to as Anderson–Pulay acceleration . This family includes the DIIS technique and its variant sometimes called commutator-DIIS, both i…
View article: A surjection theorem for maps with singular perturbation and loss of derivatives
A surjection theorem for maps with singular perturbation and loss of derivatives Open
In this paper we introduce a new algorithm for solving perturbed nonlinear functional equations which admit a right-invertible linearization, but with an inverse that loses derivatives and may blow up when the perturbation parameter \varep…
View article: Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications
Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications Open
In this paper we prove some uniform asymptotic estimates for confluent hypergeometric functions making use of the steepest-descent method. As an application, we obtain Strichartz estimates with loss of angular derivatives for the massless …
View article: Strichartz estimates for the massless radial Dirac-Coulomb equation
Strichartz estimates for the massless radial Dirac-Coulomb equation Open
We prove some Strichartz estimates for the massless, radial Dirac-Coulomb equation in 3D. The main tools in our argument are the use of a relativistic Hankel transform together with some precise estimates on the generalized eigenfunctions …
View article: Domains for Dirac–Coulomb min-max levels
Domains for Dirac–Coulomb min-max levels Open
We consider a Dirac operator in three space dimensions, with an electrostatic (i.e., real-valued) potential V(x) , having a strong Coulomb-type singularity at the origin. This operator is not always essentially self-adjoint but admits a di…
View article: A surjection theorem for singular perturbations with loss of derivatives
A surjection theorem for singular perturbations with loss of derivatives Open
In this paper we introduce a new algorithm for solving nonlinear functional equations which admit a right-invertible linearization, but such that the inverse loses derivatives. The main difference with the by now classical Nash-Moser algor…
View article: A surjection theorem for maps with singular perturbation and loss of derivatives
A surjection theorem for maps with singular perturbation and loss of derivatives Open
In this paper we introduce a new algorithm for solving perturbed nonlinear functional equations which admit a right-invertible linearization, but with an inverse that loses derivatives and may blow up when the perturbation parameter $ε$ go…
View article: A surjection theorem for maps with singular perturbation and loss of derivatives
A surjection theorem for maps with singular perturbation and loss of derivatives Open
In this paper we introduce a new algorithm for solving perturbed nonlinear functional equations which admit a right-invertible linearization, but with an inverse that loses derivatives and may blow up when the perturbation parameter $\epsi…
View article: Multiple front standing waves in the FitzHugh-Nagumo equations
Multiple front standing waves in the FitzHugh-Nagumo equations Open
There have been several existence results for the standing waves of FitzHugh-Nagumo equations. Such waves are the connecting orbits of an autonomous second-order Lagrangian system and the corresponding kinetic energy is an indefinite quadr…
View article: Local smoothing estimates for the massless Dirac-coulomb equation in 2 and 3 dimensions
Local smoothing estimates for the massless Dirac-coulomb equation in 2 and 3 dimensions Open
We prove local smoothing estimates for the massless Dirac equation with a Coulomb potential in 2 and 3 space dimensions. Our strategy of proof is inspired by a paper of Burq et al. (2003) about Schroedinger and wave equations with inverse-…