Approximations of Sobolev maps between an open set and an Euclidean sphere, boundary data, and singularities.
Approximations of solutions to nonlinear Sobolev type evolution equations.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
A-Priori Schranken für Lösungen gewisser elliptischer Probleme.
A-priori-Schranken für semi- und quasilineare parabolische Differentialgleichungen.
Aproximación clásica de la ecuación de Dirac cuando
Aproximación de un problema elíptico singular mediante elementos finitos isoparamétricos degenerados.
A-quasiconvexity : relaxation and homogenization
A-Quasiconvexity: Relaxation and Homogenization
Integral representation of relaxed energies and of Γ-limits of functionals are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p, are recovered.
A-quasiconvexity : weak-star convergence and the gap
Arbitrary growth and oscillation versus finite time blow up in nonlinear Schrödinger equations
Arbitrary high-order finite element schemes and high-order mass lumping
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elementsof order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta...
Arbitrary Lagrangian Eulerian method for compressible plasma simulations
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
We show that the critical nonlinear elliptic Neumann problem in , in , on , where is a bounded and smooth domain in , has arbitrarily many solutions, provided that is small enough. More precisely, for any positive integer , there exists such that for , the above problem has a nontrivial solution which blows up at interior points in , as . The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite-dimensional...
Area integral estimates for higher order elliptic equations and systems
Let be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in norm between the maximal function and the square function of solutions to in Lipschitz domains. Several applications of this result are discussed.
Area-minimizing integral currents with movable boundary parts of prescribed mass
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
Arithmetic features of rational conformal field theory
Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
We propose a new formulation of the 3D Boltzmann non linear operator, without assuming Grad's angular cutoff hypothesis, and for intermolecular laws behaving as 1/rs, with s> 2. It involves natural pseudo differential operators, under a form which is analogous to the Landau operator. It may be used in the study of the associated equations, and more precisely in the non homogeneous framework.