Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients

Yan Yan Li; Michael Vogelius

doi:10.1007/s002050000082

Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients

Yan Yan Li, Michael Vogelius

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

232 Scopus citations

Abstract

In this paper we derive global W^1,∞ and piecewise C^1,α estimates for solutions to divergence form elliptic equations with piecewise Hölder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.

Original language	English (US)
Pages (from-to)	91-151
Number of pages	61
Journal	Archive For Rational Mechanics And Analysis
Volume	153
Issue number	2
DOIs	https://doi.org/10.1007/s002050000082
State	Published - Jun 20 2000

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s002050000082

Cite this

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title = "Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients",

abstract = "In this paper we derive global W1,∞ and piecewise C1,α estimates for solutions to divergence form elliptic equations with piecewise H{\"o}lder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.",

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AU - Vogelius, Michael

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N2 - In this paper we derive global W1,∞ and piecewise C1,α estimates for solutions to divergence form elliptic equations with piecewise Hölder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.

AB - In this paper we derive global W1,∞ and piecewise C1,α estimates for solutions to divergence form elliptic equations with piecewise Hölder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.

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JO - Archive For Rational Mechanics And Analysis

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Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients

Abstract

All Science Journal Classification (ASJC) codes

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