An existence result for a free boundary problem for the -Laplace operator.
An existence result for an interior electromagnetic casting problem
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
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 Hadamard maximum principle for the biplacian on hyperbolic manifolds
We prove the existence of a maximum principle for operators of the type , for weights with subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure...
An improved regularity criteria for the MHD system based on two components of the solution
As observed by Yamazaki, the third component of the magnetic field can be estimated by the corresponding component of the velocity field in
An incorrectly posed problem for nonlinear elliptic equations.
An index for global Hopf bifurcation in parabolic systems.
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 inhomogeneous Dirichlet problem for a non-hypoelliptic linear partial differential operator.
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.
An iteration method for nonlinear second order evolution equations
An L¹-stability and uniqueness result for balance laws with multifunctions: a model from the theory of granular media
We study the uniqueness and L¹-stability of the Cauchy problem for a 2 × 2 system coming from the theory of granular media [9,10]. We work in a class of weak entropy solutions. The appearance of a multifunction in a source term, given by the Coulomb-Mohr friction law, requires a modification of definition of the weak entropy solution [5,6].
An observability estimate for parabolic equations from a measurable set in time and its applications
This paper presents a new observability estimate for parabolic equations in , where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.