On L<SUP>p</SUP>-Resolvent Estimates for Second-Order Elliptic Equations in Divergence Form

초록

We consider the Dirichlet problems for second-order linear elliptic equations in divergence form. The leading coefficient A has small BMO semi-norm and first-order coefficient b belongs to L-r, where nr< if n 3 and 2<r< if n =2. We first establish L-p-resolvent estimates on bounded domains having small Lipschitz constant when r/(r-1)<p<. Under the additional assumption div A L-r, we also establish L-p-resolvent estimates on bounded domains with C-1,C-1 boundary when 1 < p < r.

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