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A sharp Hölder estimate for elliptic equations in two variables

Published online by Cambridge University Press:  12 July 2007

Tonia Ricciardi
Tonia Ricciardi
Affiliation:
Dipartimento di Matematica e Applicazioni, Universitá di Napoli Federico II, Via Cintia, 80126 Naples, Italy ([email protected])
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Abstract

We prove a sharp Hölder estimate for solutions of linear, two-dimensional, divergence-form, elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has unit determinant. Our result extends some previous work by Piccinini and Spagnolo. The proof relies on a sharp Wirtinger type inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 1 , February 2005 , pp. 165 - 173
Copyright
Copyright © Royal Society of Edinburgh 2005

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