On weighted estimated for some systems of partial differential operators
Overdetermined problems and the -Laplacian.
Propriétés de quelques quadratares déduites de l'intégration des expressions differéntielles à deux variables.
Régularité analytique globale des solutions du problème de Neumann pour l’opérateur
Regularity in elliptic free boundary problems. II. Equations of higher order
Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds
Consider a flat symplectic manifold , , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If is an eigenvalue of the symplectic Dirac operator such that is not a symplectic Killing number, then is an eigenvalue of the symplectic Rarita-Schwinger operator.
Résolubilité et hypoellipticité de systèmes surdéterminés
Simplifying numerical solution of constrained PDE systems through involutive completion
When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations...
Simplifying numerical solution of constrained PDE systems through involutive completion
When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations...
Some generalizations in the mathematical developments of the theory of the geodetic overdetermined problems.
Two particular cases of the overdetermined gravimetry-gradiometry problem are discussed: (i) the case of a latitude-dependant statistical weight for gradiometric data, corresponding to a data distribution coming from satellite polar orbits, (ii) the case of a volume distribution, instead of a surface distribution, for satellite gradiometric data. In both cases a discussion of numerical methods for solving the problem with realistic data is started; for case (i), an analytic solution is found under...
Some results on the Pompeiu problem.
Sur la -fonction
Sur la résolubilité locale des équations d'Einstein
Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope
En utilisant la version de Spencer-Goldschmidt du théorème de Cartan-Kähler nous étudions les conditions nécessaires et suffisantes pour qu’un système d’équations différentielles ordinaires du second ordre soit le système d’Euler-Lagrange associé à un lagrangien régulier. Dans la thèse de Z. Muzsnay cette technique a été déjà appliquée pour donner une version moderne du papier classique de Douglas qui traite le cas de la dimension 2. Ici nous considérons le cas où la dimension est arbitraire, nous...
Two symmetry problems in potential theory.
Ueber die Integration simultaner partieller Differentialgleichungen der ersten Ordnung mit derselben unbekannten Function.
Unique continuation in abstract pseudoconcave manifolds
Varietà generiche rispetto a sistemi differenziali
Zur simultanen Integration linearer partieller Differentialgleichungen
О гомеоморфном решении многомерного аналога уравнения Бельтрами