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Local $ \mathbf{L}^{1}$ estimates for elliptic systems of complex vector fields


Authors: J. Hounie and T. Picon
Journal: Proc. Amer. Math. Soc. 143 (2015), 1501-1514
MSC (2010): Primary 35J46, 46E35; Secondary 35F05, 35N10
DOI: https://doi.org/10.1090/S0002-9939-2014-12219-2
Published electronically: December 9, 2014
MathSciNet review: 3314065
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Abstract: In this paper we present a strong local version of the Gagliardo-Nirenberg estimate that holds for elliptic systems of vector fields with smooth complex coefficients. We also consider $ L^1$ estimates on forms analogous to those known in the case of the de Rham complex on $ \mathbb{R}^N$.


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Additional Information

J. Hounie
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brazil
Email: hounie@dm.ufscar.br

T. Picon
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brazil
Address at time of publication: Departamento de Computação e Matemática, Universidade de São Paulo, Ribeirão Preto, SP, 14040-901, Brazil
Email: picon@dm.ufscar.br, picon@ffclrp.usp.br

DOI: https://doi.org/10.1090/S0002-9939-2014-12219-2
Received by editor(s): August 11, 2012
Published electronically: December 9, 2014
Additional Notes: This work was supported in part by CNPq and FAPESP
Communicated by: James E. Colliander
Article copyright: © Copyright 2014 American Mathematical Society