$ L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations
Yu. A. Alkhutov · Sbornik Mathematics · 1998
The Dirichlet problem for second-order divergence-form elliptic equations with coefficients continuous in a closed domain is considered. A necessary and sufficient condition on the boundary of a compact domain ensuring the unique -solubility of the problem in question and also a corresponding coercive -estimate for all 1$ SRC=http://ej.iop.org/images/1064-5616/189/1/A01/tex_sm_287_img2.gif/> are obtained.