Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities.
Quasiconvexity at the boundary and concentration effects generated by gradients
We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251–277]. As a consequence we get...
Quelques méthodes d'étude de la propagation d'oscillations hyperboliques non linéaires
Quenching for a reaction-diffusion system with coupled inner singular absorption terms.
Radial minimizers of a Ginzburg-Landau functional.
Radiation fields
We study the “hyperboloidal Cauchy problem” for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behavior at the boundary, or with polyhomogeneous initial data. Specifically, we consider nonlinear symmetric hyperbolic systems of a form which includes scalar fields with a nonlinearity, as well as wave maps, with initial data given on a hyperboloid; several of the results proved apply to general space-times admitting conformal...
Random data Cauchy problem for supercritical Schrödinger equations
Random walks on graphs with volume and time doubling.
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
Reaction-diffusion in nonsmooth and closed domains.
Reaction-diffusion systems with 1-homogeneous non-linearity.
Regular regions for parabolic and elliptic equations
Remarks relevant to classical maximum principles.
Remarques sur des résultats d'existence pour les équations de Hamilton-Jacobi du premier ordre
Résultats d'existence et de non-existence pour la solution positive et bornée d'une e.d.p. elliptique non linéaire
Résultats d'existence pour certains problèmes elliptiques quasilinéaires
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Riccati inequality and oscillation criteria for PDE with -Laplacian.
Riccati-type inequality and oscillation criteria for a half-linear PDE with damping.
Rigorous numerics for the Cahn-Hilliard equation on the unit square.
Risultati di esistenza, regolarità e confronto per equazioni ellittiche