Sur l'existence de solutions analytiques globales des équations aux dérivées partielles linéaires à coefficients constants en deux variables indépendantes, d'après E. de Giorgi
Sur quelques problèmes à frontière libre analytique dans le plan
Systems of meromorphic microdifferential equations
We introduce the notion of system of meromorphic microdifferential equations. We use it to prove a desingularization theorem for systems of microdifferential equations.
Syzygies of modules and applications to propagation of regularity phenomena.
Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.
Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux
The blow-up curve of solutions of mixed problems for semilinear wave equations with exponential nonlinearities in one space dimension, II
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and well-posedness (Levi condition).
The change in electric potential due to lightning
The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the...
The Dirichlet problem and weighted spaces. II.
The Isolated Point Singularity Problem for the Coupled Yang-Mills Equations in Higher Dimensions.
The space of exponentially decreasing entire functions and its application to solvability
Transformations de Laplace sur des sous-variétés de et représentations d’ondes entrantes et sortantes
Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz equation.
Unicité du problème de Cauchy pour des opérateurs elliptiques
Unicité pour les équations non linéaires du premier ordre
Uniqueness and regularity properties of linear operators and their applications
Valeurs propres d'une classe d'équations différentielles singulières sur une demi-droite
Well posedness under Levi conditions for a degenerate second order Cauchy problem
Асимптотическое поведение решения краевой задачи в перфорированной области с осциллирующей границей.
Задача Дирихле для эллиптической по Петровскому системы уравнений второго порядка.