A refinement of the Poincaré inequality for Kolmogorov operators on .
A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations
A regularity result for p-harmonic equations with measure data.
We examine the p-harmonic equation div |grad u|(p-2). grad u = mu, where mu is a bounded Radon measure. We determine a range of p's for which solutions to the equation verify an a priori estimate. For such p's we also prove a higher integrability result.
A remark on a Harnack inequality for degenerate parabolic equations
A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity
A sharp Strichartz estimate for the wave equation with data in the energy space
We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the norm of the solution in terms of the energy. We also characterise the maximisers.
A spherical Harnack inequality for singular solutions of nonlinear elliptic equations
A stability estimate for a solution to the wave equation with the Cauchy data on a timelike cylindrical surface.
A stability result for -harmonic systems with discontinuous coefficients.
A supersolution-subsolution method for nonlinear biharmonic equations in
A survey of results on nonlinear Venttsel problems
We review the recent results for boundary value problems with boundary conditions given by second-order integral-differential operators. Particular attention has been paid to nonlinear problems (without integral terms in the boundary conditions) for elliptic and parabolic equations. For these problems we formulate some statements concerning a priori estimates and the existence theorems in Sobolev and Hölder spaces.
A Theorem on Elliptic Differential Inequalities with an Application to Gradient Bounds.
A W 2, 2 Bound for a Class of Elliptic Equations in Nondivergence Form with Rough Coefficients.
About a Variant of the Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation"
This is a report on project initiated with Anne Nouri [3], presently in progress, with the collaboration of Nicolas Besse [2] ([2] is mainly the material of this report) . It concerns a version of the Vlasov equation where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full non linear problem and also on natural connections with several other equations of mathematical physic.
About some types of boundary value problems with interfaces
About the Morse Theory for Certain Variational Problems.
Absorption effects for some elliptic equations with singularities
We give an expository review of recent results obtained for elliptic equations having natural growth terms of absorption type and singular data. As a new result, we provide an application to the case of lower order terms of subcritical growth, proving a general solvability result with measure data for a class of equations modeled on (1.6).
Aleksandrov-type estimates for a parabolic Monge-Ampère equation.
An age-dependent model describing the spread of panleucopenia virus within feline populations
Global existence results and long time behavior are provided for a mathematical model describing the propagation of Feline Panleucopenia Virus (FPLV) within a domestic cat population; two transmission modes are involved: a direct one from infective cats to susceptible ones, and an indirect one from the contaminated environment to susceptible cats. A more severe impact of the virus on young cats requires an age-structured model.
An Ambrosetti-Prodi-type problem for an elliptic system of equations via monotone iteration method and Leray-Schauder degree theory.