An effective method for the existence of the global attractor of a nonlinear wave equation.
An eigenvalue problem related to Hardy’s inequality
An Elementary Proof of Harnack's Inequality for Schrödinger Operators and Related Topics.
An elliptic semilinear equation with source term involving boundary measures: the subcritical case.
We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2),⎧ Δu + uq = 0, in Ω⎨⎩ u = μ, on ∂Ωwhere 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted Marcinkiewicz spaces.
An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.
We prove a commutator inequality of Littlewood-Paley type between partial derivatives and functions of the Laplacian on a Lipschitz domain which gives interior energy estimates for some BVP. It can be seen as an endpoint inequality for a family of energy estimates.
An equation for the limit state of a superconductor with pinning sites.
An estimate for solutions to the Schrödinger equation.
An estimate on convergence for an homogeneisation problem for variational inequalities
An existence criterion for -norms of higher-order derivatives of solutions to a homogeneous parabolic equation.
An Existence Theorem for Class of Non-Coercive Optimization and Variational Problems.
An existence theorem for the v. Kármán equations under the condition of free boundary
An inequality for integrals
An inequality of the 1-D Klein-Gordon equation with a time-varying parameter.
An inequality on solutions of heat equation.
An Ingham type proof for a two-grid observability theorem
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
An Ingham type proof for a two-grid observability theorem
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418]. Our proof follows an Ingham type approach.
An initial and boundary value problem for nonlinear composite type systems of three equations.
An Initial-Boundary-Value Problem for a Certain Density-Dependent Diffusion System.
An integral estimate for weak solutions to some quasilinear elliptic systems
We prove an integral estimate for weak solutions to some quasilinear elliptic systems; such an estimate provides us with the following regularity result: weak solutions are bounded.
Analogue d'un Lemme de Kohn et Nirenberg