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The conjugate Beltrami equation with coefficient in Morrey spaces

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Abstract

In this paper we study the distributional (and quasiregular) solutions of the conjugated Beltrami equation when the coefficient has distributional partial derivatives in Morrey spaces. In this sense, we show that the solutions have second partial derivatives in other Morrey spaces.

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References

  1. Astala, K., Iwaniec, T., Martin, G.: Elliptic Equations and Quasiconformal Mappings in the Plane. Princeton Mathematical Series, vol. 47. Princeton University Press, Princeton (2009)

    MATH  Google Scholar 

  2. Astala, K., Iwaniec, T., Saksman, E.: Beltrami operators in the plane. Duke Math. J. 107(1), 27–56 (2001)

    Article  MathSciNet  Google Scholar 

  3. Clop, A., Cruz, V.: Weighted estimates for Beltrami equations. Ann. Acad. Sci. Fenn. Math. 38(1), 91–113 (2013)

    Article  MathSciNet  Google Scholar 

  4. Clop, A., Faraco, D., Mateu, J., Orobitg, J., Zhong, X.: Beltrami equations with coefficient in the Sobolev Space \(W^{1, p}\). Publ. Mat. 53, 197–230 (2009)

    Article  MathSciNet  Google Scholar 

  5. Cruz, V., Mateu, J., Orobitg, J.: Beltrami equation with coefficient in Sobolev and Besov spaces. Can. J. Math. 65, 1217–1235 (2013)

    Article  MathSciNet  Google Scholar 

  6. Iwaniec, T.: \(L^p\)-theory of quasiregular mappings. In: Quasiconformal Space Mappings, Volume 1508 of Lecture Notes in Mathematics, pp. 39–64. Springer, Berlin (1992)

    Chapter  Google Scholar 

  7. Koski, A.: Singular integrals and Beltrami type operators in the plane and beyond. Master Thesis, Department of Mathematics, University of Helsinki (2011)

  8. Petermichl, S., Volberg, A.: Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular. Duke Math. J. 112(2), 281–305 (2002)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We would like to thank the anonymous reviewers for their suggestions and comments. Also, the authors wishes to thank the CONACyT and PRODEP-SEP for financial support.

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Authors and Affiliations

  1. Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Ciudad de México, Mexico

    Antonio L. Baisón Olmo & Victor A. Cruz Barriguete

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  1. Antonio L. Baisón Olmo
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  2. Victor A. Cruz Barriguete
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Correspondence to Victor A. Cruz Barriguete.

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Baisón Olmo, A.L., Cruz Barriguete, V.A. The conjugate Beltrami equation with coefficient in Morrey spaces. Collect. Math. 71, 93–102 (2020). https://doi.org/10.1007/s13348-019-00249-2

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  • DOI: https://doi.org/10.1007/s13348-019-00249-2

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