Abstract
In this paper, we establish gradient estimates in Morrey spaces and Holder 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 X1, . . . , Xq are real smooth vector fields satisfying Hormander’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 Xα.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have