An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

A Monomial-by-Monomial Method for Computing Regular Solutions of Systems of Pseudo-Linear Equations

This paper deals with the local analysis of systems of pseudo-linear equations. We define regular solutions and use this as a unifying theoretical framework for discussing the structure and existence of regular solutions of various systems of linear functional equations. We then give a generic and flexible algorithm for the computation of a basis of regular solutions. We have implemented this algorithm in the computer algebra system Maple in order to provide novel functionality for solving systems of linear differential, difference and q-difference equations given in various input formats.     

Optimal regularity for [`(?)] b\bar \partial _b on CR manifoldson CR manifolds

In this paper a new explicit integral formula is derived for solutions of the tangential Cauchy-Riemann equations on CR q-concave manifolds and optimal estimates in the Lipschitz norms are obtained.     

Characterization of regular singular linear systems of difference equations

This paper deals with linear systems of difference equations whose coefficients admit generalized factorial series representations atz=. We are concerned with the behavior of solutions near the pointz= (the only fixed singularity for difference equations). It is important to know whether a system of linear difference equations has a regular singularity or an irregular singularity. To a given system () we can assign a number , called the Moser's invariant of (), so that the system is regular singular if and only if 1. We shall develop an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations to an irreducible form. The computation ot the number can be done explicitly from this irreducible form.     

Gevrey character of formal solutions of differential—difference equations with polynomials coefficients

In this paper we prove that formal factorial series as well as formal power series in 1/x solutions of a differential—difference equation with polynomial coefficients are Gevrey of some order which can be determined from a suitable Newton polygon     

Matrices of Scalar Differential Operators: Divisibility and Spaces of Solutions

Computational Mathematics and Mathematical Physics - We investigate the connection between divisibility of full-rank square matrices of linear scalar differential operators over some differential...     

An existence result for an interior electromagnetic casting problem

This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C ². Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.     

Triangulable locally nilpotent derivations in dimension three

In this paper we give an algorithm to recognize triangulable locally nilpotent derivations in dimension three. In case the given derivation is triangulable, our method produces a coordinate system in which it exhibits a triangular form.     

Régularité höldérienne du ∂¯b dans les hypersurfaces 1-convexes-concaves

Ohne Zusammenfassung Received 15 October 1993; in final form 15 August 1994