L-p-REGULARITY RESULTS FOR 2m-TH ORDER PARABOLIC EQUATIONS IN TIME-VARYING DOMAINS

摘要

This paper is devoted to the analysis of the following linear 2m-th order parabolic equation partial derivative(t)u+(-1)(m) Sigma(N)(K=1) partial derivative(2m)(xk) u = f, subject to Dirichlet type condition partial derivative(l)(v)u = 0, l = 0,1, ..., m-1, on the lateral boundary, where m is a positive integer. The right-hand side f of the equation is taken in the Lebesgue space L-p, 1 1/2m.