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E. Bonnetier (1)
Abstract : 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 Hölder class C-gamma for some positive exponent gamma
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