Volume 6, Issue 4
Lp-estimates for the Strong Solutions of Elliptic Equations of Nondivergent Type

Bian Baojun

J. Part. Diff. Eq.,6(1993),pp.349-360

Published online: 1993-06

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  • Abstract
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

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@Article{JPDE-6-349, author = {Bian Baojun}, title = {Lp-estimates for the Strong Solutions of Elliptic Equations of Nondivergent Type}, journal = {Journal of Partial Differential Equations}, year = {1993}, volume = {6}, number = {4}, pages = {349--360}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5721.html} }
TY - JOUR T1 - Lp-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.
Bian Baojun. (1970). Lp-estimates for the Strong Solutions of Elliptic Equations of Nondivergent Type. Journal of Partial Differential Equations. 6 (4). 349-360. doi:
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