On Boolean partial differential equations
On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes
On the existence of global holomorphic solutions of differential equations with complex parameters
On the linear force-free fields in bounded and unbounded three-dimensional domains
Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.
On the solvability of the equation div in and in
We show that the equation div has, in general, no Lipschitz (respectively ) solution if is (respectively ).
Periodic solutions to linear partial differential equations of the first order
Propagation des singularités pour des problèmes aux limites
Solutions indéfiniment différentiables d’un système d’équations aux différences et application aux systèmes d’équations aux dérivées partielles
Dans cette note, nous prouvons l’existence de solutions indéfiniment différentiables d’un système de deux équations aux différences et appliquons la technique utilisée à l’étude des systèmes d’équations linéaires aux dérivées partielles.Dans chaque cas, on montre que les solutions sont les premières composantes des solutions d’un système matriciel que nous étudions.
Solutions of Analytical Systems of Partial Differential Equations
In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).
Solutions of the equation
Solutions which are flat or Singular on Totally Characteristic Manifolds of first order Partial Differential Equations
Solvability near the characteristic set for a class of planar vector fields of infinite type
We study the solvability of equations associated with a complex vector field in with or coefficients. We assume that is elliptic everywhere except on a simple and closed curve . We assume that, on , is of infinite type and that vanishes to a constant order. The equations considered are of the form , with satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of is , the equation is solvable in the category but not in the category....
Some aspects of holomorphic approximations from the point of view of PDEs
Some partial differential equations in Clifford analysis
Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.
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.
Spectral analysis of strongly propagative systems.
Sulle soluzioni di equazioni alle derivate parziali del primo ordine in insiemi di perimetro finito con termine noto misura
Sur la résolubilité locale et l'intégrabilité locale de systèmes de champs vectoriels
Sur les Champs de vecteurs peu réguliers
The general method for solving of the boundary problems for the partial differential equations of any order II