Some remarks on -valued functions
Some remarks on multidimensional systems of conservation laws
This note is concerned with the Cauchy problem for hyperbolic systems of conservation laws in several space dimensions. We first discuss an example of ill-posedness, for a special system having a radial symmetry property. Some conjectures are formulated, on the compactness of the set of flow maps generated by vector fields with bounded variation.
Some remarks on Prandtl system
The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed.
Some remarks on the asymptotic equivalence
Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations
This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Some remarks on the boundary regularity for minima of variational problems with obstacles.
Some remarks on the continuity equation
This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.
Some remarks on the Galerkin approximation of parabolic equations
Some Remarks on the Homogenization of the Dam Problem.
Some remarks on the KP system of the Camassa-Holm hierarchy.
Some remarks on the multi-dimensional Borg-Levinson theorem
Some remarks on the Navier-Stokes equations with regularity in one direction
We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements.
Some remarks on the non-uniqueness of the stationary solutions of Navier-Stokes equations.
Some remarks on the number of solutions of some nonlinear elliptic problems
Some remarks on the regularity of minimizers of integrals with anisotropic growth
We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.
Some remarks on the regularity of weak solutions of degenerate elliptic systems.
Some remarks on the Weyl asymptotics by the approximate spectral projection method
In questo lavoro studiamo il resto relativo della formula asintotica per gli autovalori di un operatore differenziale in , ottenuta mediante il metodo delle proiezioni spettrali approssimate ([3], Theorem 6.2). In un primo tempo diamo un controesempio di un operatore di Schrödinger con potenziale a crescita algebrica, per il quale il resto non è limitato. Quindi specifichiamo alcune condizioni addizionali da imporre all'operatore in modo da avere un resto infinitesimo.
Some remarks on time-dependent evolution systems in the hyperbolic case
Some Remarks on Transmutation, Scattering Theory, and Special Functions.
Some remarks on two-scale convergence and periodic unfolding
The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization...