About mathematical model or some diffuse processes in the Mediterranean and exterior Poincare problem for the Helmholtz equation.
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 the Morse Theory for Certain Variational Problems.
About Uniqueness for Nonlinear Boundary Value Problems.
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.
Absence of local and global solutions to an elliptic system with time-fractional dynamical boundary conditions.
Absence of positive eigenvalues for a class of subelliptic operators.
Absence of Positive Eigenvalues in a Class of Multiparticle Quantum Systems.
Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others.
Absolute continuity of the spectrum of periodic operators of mathematical physics
The lecture is devoted to the problem of absolute continuity of the spectrum of periodic operators. A general approach to this problem was suggested by L. Thomas in 1973 for the case of the Schrödinger operator with periodic electric potential. Further application of his method to concrete operators of mathematical physics met analytic difficulties. In recent years several new problems in this area have been solved. We propose a survey of known results in this area, including very recent, and formulate...
Absolutely continuous spectrum and scattering in the surface Maryland model
We study the discrete Schrödinger operator in with the surface quasi periodic potential , where . We first discuss a proof of the pure absolute continuity of the spectrum of on the interval (the spectrum of the discrete laplacian) in the case where the components of are rationally independent. Then we show that in this case the generalized eigenfunctions have the form of the “volume” waves, i.e. of the sum of the incident plane wave and reflected from the hyper-plane waves, the form...
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).
Abstract quasi-variational inequalities of elliptic type and applications
A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators...
Acceleration of Convergence for Finite Element Solutions of the Poisson Equation.
Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive...
Adaptive coupling of boundary elements and finite elements
Adaptive finite element methods for elliptic problems: Abstract framework and applications
We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space V that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into V. We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete problems...