Partial differential equations with non-Euclidean geometries

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2008Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems - S, volume 1, pages 481-504 (issn: 1937-1632, eissn: 1937-1179,

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Authors: Herbert Koch;

doi: 10.3934/dcdss.2008.1.481

Partial differential equations with non-Euclidean geometries

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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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