About one high-order linear equation of mixed type.
About some types of boundary value problems with interfaces
About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces...
About stability of equilibrium shapes
About stability of equilibrium shapes
We discuss the stability of "critical" or "equilibrium" shapes of a shape-dependent energy functional. We analyze a problem arising when looking at the positivity of the second derivative in order to prove that a critical shape is an optimal shape. Indeed, often when positivity -or coercivity- holds, it does for a weaker norm than the norm for which the functional is twice differentiable and local optimality cannot be a priori deduced. We solve this problem for a particular but significant example....
About steady transport equation I – -approach in domains with smooth boundaries
We investigate the steady transport equation in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular stress is put onto the problem to extend the results to as less regular vector fields , as possible (conserving the requirement of...
About steady transport equation. II: Schauder estimates in domains with smooth boundaries.
About the decay of surface waves on viscous fluids without surface tension
We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.
About the existence and uniqueness of solution to fractional Bürger's equation.
About the existence and uniqueness theorem for hyperbolic equation.
About the influence of oscillations on Strichartz-type decay estimates.
About the interface of some nonlinear diffusion problems.
About the Morse Theory for Certain Variational Problems.
About the representation of solutions of linear elliptic equations of arbitrary order
About the Symposium, Foreword, Contents
About Uniqueness for Nonlinear Boundary Value Problems.
Abrupt and smooth separation of free boundaries in flow problems
Abschätzung nach unten für Lösungen nichtlinearer Differentialungleichungen
Absence de principe du maximum pour certaines équations paraboliques complexes
Le but de cette note est de montrer que le principe du maximum, même dans une version affaiblie, n’est pas vérifıé pour la classe des opérateurs paraboliques du type , où L est un opérateur différentiel elliptique d’ordre 2 sous forme divergence à coefficients complexes mesurables et bornés en dimension supérieure ou égale à 5. Le principe de démonstration repose sur un résultat abstrait de la théorie des semi-groupes permettant d’utiliser le contre-exemple présenté dans [MNP] à la régularité des...
absence de résonance près du réel pour l’opérateur de Schrödinger
On donne dans cet exposé des bornes inférieures universelles, en limite semiclassique, de la hauteur des résonances de forme associées aux opérateurs de Schrödinger à l’extérieur d’obstacles avec des conditions au bord de Dirichlet ou de Neumann et des potentiels analytiquement dilatables et tendant vers à l’infini. Ces bornes inférieures sont exponentiellement petites par rapport à la constante de Planck.