On the Davey-Stewartson systems
On the envelope of regularity for solutions of homogeneous systems of linear partial differential operators
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the Existence of Real Analytic Solutions of Partial Differential Equations with Constant Coefficients.
On the Functional Dimension of Solution Spaces of Hypoelliptic Partial Differential Operators.
On the functors Ext¹(E,F) for Fréchet spaces
On the "Fundamental Principle" of L. Ehrenpreis
On the global solvability of linear partial differential equations with constant coefficients in the space of real analytic functions
This article surveys results on the global surjectivity of linear partial differential operators with constant coefficients on the space of real analytic functions. Some new results are also included.
On the hyperbolicity of a third order operator and the generalized Goursat-Darboux problem
On the Influence of Lower Order Terms for Propagation of Analytic Singularities for Operators with Constant Coefficients.
On the Operator Solutions of Difference Equations
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data . The analytic initial data can be extended as holomorphic functions in a strip around the -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
On the singularities of solutions of partial differential equations with constant coefficients
On variational approach to the Hamilton-Jacobi PDE
In this paper we construct a minimizing sequence for the problem (1). In particular, we show that for any subsolution of the Hamilton-Jacobi equation there exists a minimizing sequence weakly convergent to this subsolution. The variational problem (1) arises from the theory of computer vision equations.
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
Ouverts concaves et théorèmes de dualité pour les systèmes différentiels à coefficients constants
Ouverts stablement convexes par rapport à un opérateur différentiel
On montre l’équivalence entre certaines inégalités “à la Carleman” et certaines propriétés de régularité des solutions à support compact d’équations aux dérivées partielles à coefficients constants : étant un opérateur différentiel sur , on en déduit une caractérisation, en termes d’inégalités , des ouverts de tels que soit -convexe pour tout entier .
Overdetermined hyperbolic systems on l.e. convex sets