摘要 : We consider the Dirichlet problem [GRAPHICS] for two second-order elliptic operators L(k)u = Sigma(i,j=1)(n) a(k)(i,j)(x) partial derivative(ij)u(x), k = 0,1, in a bounded Lipschitz domain D subset of R-n. The coefficients a(k)(i,... 展开 We consider the Dirichlet problem [GRAPHICS] for two second-order elliptic operators L(k)u = Sigma(i,j=1)(n) a(k)(i,j)(x) partial derivative(ij)u(x), k = 0,1, in a bounded Lipschitz domain D subset of R-n. The coefficients a(k)(i,j) belong to the space of bounded mea oscillation BMO with a suitable small BMO modulus. We assume that L-0 is regular in L-p (partial derivativeD, dsigma) for some p, 1 < &INFIN;, that is, &PAR;Nu&PAR;L-p &LE; C &PAR;g&PAR;L-p for all continuous boundary data g. Here &sigma; is the surface measure &PARTIAL;D and Nu is the nontangential maximal operator. The aim of this paper is to establish sufficient conditions on the difference of the coefficients &epsilon;(i,j)(x) = a(1)(i,j)(x) - a(o)(i,j)(x) that will assure the perturbed operator L-1 to be regular in L-q (partial derivativeD, dsigma) for some q, 1 < q < infinity. [References: 28] 收起