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- W2021298673 abstract "In this paper we consider the elliptic equation $nabla cdot anabla u= 0$ in a two dimensional domain $Omega$, 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 $Omega$ 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 $W^{1,infty}$. 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 $gamma$." @default.
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- W2021298673 date "2000-01-01" @default.
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- W2021298673 title "An Elliptic Regularity Result for a Composite Medium with Touching Fibers of Circular Cross-Section" @default.
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- W2021298673 doi "https://doi.org/10.1137/s0036141098333980" @default.
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