CENTRE DE MATHEMATIQUES APPLIQUEES 
         C.M.A.P.  

An improved elliptic regularity result for a composite medium with ``touching'' fibers
Eric BonnetierMichael Vogelius

In this paper we consider the elliptic equation div(a grad u) = 0
in a two dimensional domain Omega, which contains a finite number of 
circular inhomogeneities (cross-sections of fibers). 

    The coefficient, a, takes on two constant values, one on all the 
inhomogeneities and one on the part of Omega which lies outside the 
inhomogeneities. A number of the inhomogeneities may possibly touch, 
and  in spite of this we prove that any variational solution u (with 
sufficiently smooth boundary data) has a bounded gradient. For this 
very interesting, particular type of coefficient  our result improves  
a classical regularity result due to DeGiorgi and Nash, which asserts 
that the solution is in the H\"older class C-gamma for some positive
exponent gamma

The whole paper is available as a compressed Postscript file by internet
procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100)
in the directory pub/RI/1998 under the name

        bonnetier_vogelius_375.mars.ps

or by Netscape or any other www client
via the CMAP www server http://www.cmap.polytechnique.fr