Lp-estimates for the Strong Solutions of Elliptic Equations of Nondivergent Type (Journal of Partial Differential Equations, 2020)
We investigate the second derivatives L^p-estimates for the strong solutions of second order linear elliptic equations in nondivergencc form Lu = f in the case in which the leading coefficients of L are not continuous. The L^p-estimates for small p are obtained if L is uniformly elliptic. Furthermore, if the leading coefficients of L belong to W^{1,n}, then we get the second derivatives L^p-estimates for large p. The existence of the strong solutions of the homogeneous Dirichlet problem is also considered.
Keywords: Second derivatives L^p-estimates; strong solutions; discontinuous leading coefficients; perturbation technique; elliptic equations