TY - JOUR
T1 - <em>L<sup>p</sup></em>-estimates for the Strong Solutions of Elliptic Equations of Nondivergent Type
AU - Bian Baojun
JO - Journal of Partial Differential Equations
VL - 4
SP - 349
EP - 360
PY - 1993
DA - 1993/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5721.html
KW - Second derivatives L^p-estimates
KW -  strong solutions
KW -  discontinuous leading coefficients
KW -  perturbation technique
KW -  elliptic equations
AB -  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.