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Schiffer problem and isoparametric hypersurfaces.

Vladimir E. Shklover (2000)

Revista Matemática Iberoamericana

The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold and also...

Simplifying numerical solution of constrained PDE systems through involutive completion

Bijan Mohammadi, Jukka Tuomela (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

Bijan Mohammadi, Jukka Tuomela (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

F. Sacerdote, F. Sansò (1990)

Revista Matemática de la Universidad Complutense de Madrid

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...

Sur la b -fonction

M. Kashiwara (1974/1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope

Joseph Grifone, Zoltán Muzsnay (1999)

Annales de l'institut Fourier

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...

Symmetry of minimizers with a level surface parallel to the boundary

Giulio Ciraolo, Rolando Magnanini, Shigeru Sakaguchi (2015)

Journal of the European Mathematical Society

We consider the functional ℐ Ω ( v ) = ∫ Ω [ f ( | D v | ) - v ] d x , where Ω is a bounded domain and f is a convex function. Under general assumptions on f , Crasta [Cr1] has shown that if ℐ Ω admits a minimizer in W 0 1 , 1 ( Ω ) depending only on the distance from the boundary of Ω , then Ω must be a ball. With some restrictions on f , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...

Systems of meromorphic microdifferential equations

Orlando Neto (1996)

Banach Center Publications

We introduce the notion of system of meromorphic microdifferential equations. We use it to prove a desingularization theorem for systems of microdifferential equations.

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