Méthodes de factorisation dans les problèmes de convexité
Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory
A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous...
On extensions of the Mittag-Leffler theorem
The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
On homogeneous rotation invariant distributions and the Laplace operator
On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions.
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the singularities of solutions of partial differential equations with constant coefficients
One-parameter semigroups in the convolution algebra of rapidly decreasing distributions
The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that is the generating distribution of an i.d.c.s. if and only if the operator on satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.
Opérateurs différentiels bi-invariants sur un groupe de Lie
Operatori differenziali a coefficienti costanti di tipo iperbolico-(ipo)ellittico
Parameterintegration zur Berechnung von Fundamentallösungen [Book]
Partial differential operators depending analytically on a parameter
Let be a differential operator with constant coefficients depending analytically on a parameter . Assume that the family P(,D) is of constant strength. We investigate the equation where is a given analytic function of with values in some space of distributions and the solution is required to depend analytically on , too. As a special case we obtain a regular fundamental solution of P(,D) which depends analytically on . This result answers a question of L. Hörmander.
Propagation des singularités pour une classe d'opérateurs à caractéristiques multiples et résolubilité locale
On considère des opérateurs à caractéristiques de multiplicité constante et à partie principale réelle. Avec une hypothèse, dite condition de Lévi, sur les termes d’ordre inférieur, on étend à ces opérateurs le théorème de Duistermaat-Hörmander sur l’invariance par le flot hamiltonien du spectre singulier des solutions de . Un point essentiel réside dans la preuve de l’invariance de la condition de Lévi par transformation canonique. On donne une application à la résolubilité locale de ce type...
Representation of Green's function for the Dirichlet problem of polyharmonic equations in a ball.
Résolubilité sur un espace riemannien symétrique
Solutions analytiques des équations aux dérivées partielles à coefficients constants
Solutions élémentaires invariantes
Spectral decomposition of Green’s integrals and existence of -solutions of matrix factorizations of the Laplace operator in a ball
Sur les équations invariantes par un groupe
Sur l'existence de solutions analytiques d'équations à coefficients constants