Partial differential equations with non-Euclidean geometries

Herbert Koch

doi:10.3934/dcdss.2008.1.481

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2008, Volume 1, Issue 3: 481-504. Doi: 10.3934/dcdss.2008.1.481

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Partial differential equations with non-Euclidean geometries

Herbert Koch^1,

1.
Mathematisches Institut, Universität Bonn, Beringstrasse 1, D - 53115 Bonn

Received: January 31, 2008

Revised: February 29, 2008

Published: August 2008

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Abstract

Coifman and Weiss initiated the study of singular integral operators on spaces of homogeneous type. We study partial differential equations with a non-Euclidean geometry and we obtain weighted estimates using the theory of Muckenhoupt weights on related spaces of homogeneous type. Examples include squares of vector fields, elliptic operators with a drift and the Oseen operator.

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Mathematics Subject Classification: Primary: 45E10, 35J15; Secondary: 35Q30.

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