Fonction spectrale d'opérateurs non elliptiques
Hodge type decomposition
In the space of polynomial p-forms in ℝⁿ we introduce some special inner product. Let be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that splits as the direct sum , where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.
Implicit second order partial differential equations
Integralrelationen mit variablen Grenzen für spezielle Funktionen der mathematischen Physik.
-error analysis for a system of quasivariational inequalities with noncoercive operators.
Least regret control, virtual control and decomposition methods
"Least regret control" consists in trying to find a control which "optimizes the situation" with the constraint of not making things too worse with respect to a known reference control, in presence of more or less significant perturbations. This notion was introduced in [7]. It is recalled on a simple example (an elliptic system, with distributed control and boundary perturbation) in Section 2. We show that the problem reduces to a standard optimal control problem for augmented state equations. On...
Méthodes pour des équations aux dérivées partielles dépendant d’une infinité de variables
New optimal regularity results for infinite-dimensional elliptic equations
In questo articolo si ottengono stime di Schauder di tipo nuovo per equazioni ellittiche infinito-dimensionali del secondo ordine con coefficienti Hölderiani a valori nello spazio degli operatori Hilbert-Schmidt. In particolare si mostra che la derivata seconda delle soluzioni è Hilbert-Schmidt.
Note on operators produced by sesquilinear forms
Noyaux d'Agmon
Numerical methods for a model for wave propagation in composite anisotropic media
On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two
In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in . We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.
On a Purely ?Riemannian" Proof of the Structure and Dimension of the Unramified Moduli Space of a Compact Riemann Surface.
On identification of critical curves
The paper deals with the problem of finding a curve, going through the interior of the domain , accross which the flux , where is the solution of a mixed elliptic boundary value problem solved in , attains its maximum.
On the Existence of Wave Operators for Dirac Operators.
On the initial value problem for a partial differential equation with operator coefficients.
On the inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation with constant coefficients of the second order
On the maximum principle in the linear-elasticity theory
On the spectral theory of pseudo-differential elliptic boundary problems
Opérateurs elliptiques et problème de Cauchy