## Abstract

In this paper we consider the elliptic equation ▽ · α▽u = 0 in a two dimensional domain Ω, which contains a finite number of circular inhomogeneities (cross-sections of fibers). The coefficient, a, takes two constant values, one in all the inhomogeneities and one in the part of Ω which lies outside the inhomogeneities. A number of the inhomogeneities may possibly touch, but in spite of this we prove that any variational solution u (with sufficiently smooth boundary data) is in W^{1,∞}. 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^{γ} for some positive exponent γ.

Original language | English (US) |
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Pages (from-to) | 651-677 |

Number of pages | 27 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - 2000 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

## Keywords

- Composite materials
- Elliptic regularity