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Estimates in generalized Morrey spaces for nondivergence degenerate elliptic operators with discontinuous coefficients

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

The purpose of this paper is to investigate the local regularity of the nondivergence degenerate elliptic operator with lower order terms in generalized Morrey spaces, structured on a family of Hörmander’s vector fields without an underlying group structure. The coefficients of the second order terms of the operator are real valued, bounded and measurable functions, such that the uniform ellipticity condition holds; moreover, they belong to the space VMO (Vanishing Mean Oscillation), with respect to the subelliptic metric induced by the vector fields. The coefficients of the lower order terms of the operator are in suitable generalized Morrey spaces.

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Authors and Affiliations

  1. Department of Applied Mathematics, Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, Northwestern Polytechnical University, Xi’an, 710129, People’s Republic of China

    Na Wei, Pengcheng Niu & Maochun Zhu

  2. School of statistics, Xi’an University of Finance and Economics, Xi’an, 710100, People’s Republic of China

    Sufang Tang

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  1. Na Wei
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  2. Pengcheng Niu
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  3. Sufang Tang
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  4. Maochun Zhu
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Correspondence to Pengcheng Niu.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant Nos. 10871157, 11001221), Specialized Research Fund for the Doctoral Program of Higher Education (No. 200806990032).

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Wei, N., Niu, P., Tang, S. et al. Estimates in generalized Morrey spaces for nondivergence degenerate elliptic operators with discontinuous coefficients. RACSAM 106, 1–33 (2012). https://doi.org/10.1007/s13398-011-0047-1

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  • DOI: https://doi.org/10.1007/s13398-011-0047-1

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