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Estimates in Morrey Spaces and Hölder Continuity for Weak Solutions to Degenerate Elliptic Systems

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Abstract

In this paper, we establish gradient estimates in Morrey spaces and Hölder continuity for weak solutions of the following degenerate elliptic system

$$-X_{\alpha}^{\ast}(a_{ij}^{\alpha\beta}(x)X_{\beta}u^{j})=g_{i}-X_{\alpha}^{\ast}f_{i}^{\alpha}(x),$$

where X 1, . . . , X q are real smooth vector fields satisfying Hörmander’s condition, coefficients \({a_{ij}^{\alpha \beta }\in VMO_X \cap L^\infty (\Omega ), \alpha,\beta=1,2, \,.\,.\,.\, ,q, i,j=1,2, \,.\,.\,.\, ,N, X_{\alpha}^{\ast}}\) is the transposed vector field of X α.

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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, Shaanxi, China

    Yan Dong & Pengcheng Niu

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  1. Yan Dong
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  2. Pengcheng Niu
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Correspondence to Pengcheng Niu.

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Dong, Y., Niu, P. Estimates in Morrey Spaces and Hölder Continuity for Weak Solutions to Degenerate Elliptic Systems. manuscripta math. 138, 419–437 (2012). https://doi.org/10.1007/s00229-011-0498-x

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  • DOI: https://doi.org/10.1007/s00229-011-0498-x

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