Results in L..(...) for the Schrödinger equation with a time-dependent potential.
Results of nonexistence of solutions for some nonlinear evolution problems
In the present paper, we prove nonexistence results for the following nonlinear evolution equation, see works of T. Cazenave and A. Haraux (1990) and S. Zheng (2004), posed in where is -fractional power of Our method of proof is based on suitable choices of the test functions in the weak formulation of the sought solutions. Then, we extend this result to the case of a system of the same type.
Results on existence of solution for an optimal design problem.
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.
Results on qualitative features of periodic solutions of KdV
Résurgence d'un thème de Huygens-Fresnel
Résurgence quantique
Retractions onto the Space of Continuous Divergence-free Vector Fields
We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset satisfying a mild geometric condition, there is no uniformly continuous representation operator for -charges in .
Return method : application to controllability
Reverse convolution inequalities and applications to inverse heat source problems.
Reverse functional inequalities and their applications to nonlinear elliptic boundary value problems.
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Revisited isoperimetric inequalities for the p-capacity and application to the muskat problem
Revisiting the method of sub- and supersolutions for nonlinear elliptic problems.
Riccati inequality and oscillation criteria for PDE with -Laplacian.
Riccati-type inequality and oscillation criteria for a half-linear PDE with damping.
Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians
We use the functorial properties of Rieffel’s pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are extracted from the quasi-orbit structure of the dynamical system. The semi-classical behavior of the families of spectra is also studied.
Riemann problem solutions that are stable to perturbation
Riemann-Hilbert problem and solvability of differential equations.
Riemannian manifolds with maximal eigenfunction growth
Riemann-Lebesgue properties of Green's functions with applications to inverse scattering.