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Articles

Weighted solution of the Dirac Beltrami equation with coefficient in VMO

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Pages 747-760 | Received 19 Mar 2015, Accepted 03 Nov 2015, Published online: 04 Jan 2016
 

Abstract

We study the generalized Beltrami equation , where is the left Dirac operator in acting on functions in and with values in the complex Clifford algebra , is its conjugate, and is a -valued function with compact support, with vanishing mean oscillation, satisfying , where are the coordinates of in . Let be a weight function in . We prove that if belongs to the Muckenhoupt class with , that makes continuous the Riesz potential , then for every , there exists a solution of the equation above satisfying for every distributional partial derivative. If , we prove the same result for any .

AMS Subject Classifications:

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Mexican grant PAPIIT-UNAM [IN102915].

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