Constructible sheaves, Whitney functions and Schwartz's distributions
Construction de solutions élémentaires dans le faisceau de M. Sato
Construction de solutions nulles et singulières pour des opérateurs de type principal
Construction de solutions ramifiées autour de deux hypersurfaces caractéristiques simples pour des opérateurs quasi-linéaires
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Construction solutions of PDE in parametric form.
Contact geometry of hyperbolic equations of generic type.
Contact geometry of hyperbolic Monge-Ampére equations.
Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions
We study the geometry of multidimensional scalar order PDEs (i.e. PDEs with independent variables), viewed as hypersurfaces in the Lagrangian Grassmann bundle over a -dimensional contact manifold . We develop the theory of characteristics of in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of . After specializing such results to general Monge-Ampère equations (MAEs), we focus our attention to MAEs of...
Contact integrable extensions and differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
Contingent solutions to the center manifold equation
Continuation of analytic solutions of linear differential equations up to convex conical singularities
Continuity of solutions to a basic problem in the calculus of variations
We study the problem of minimizing over the functions that assume given boundary values on . The lagrangian and the domain are assumed convex. A new type of hypothesis on the boundary function is introduced: thelower (or upper) bounded slope condition. This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary...
Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front sets satisfy some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is not continuous for the usual topology on , and the tensor product is not separately continuous. In this paper,...
Continuous and generalized solutions of singular partial differential equations.
Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies
In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting...
Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces.
Contributions to local and microlocal analysis, an overwiew
Control for hyperbolic equations