EXTENDING POMPEIU OPERATOR AND THE COMPACTNESS OF SOLUTION SET FOR A CLASS OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

摘要

This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev’s sense, a;（x）,i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded and measurable in a bounded multiply connected domain Ω, the boundary S is as-sumed to be sufficiently smooth, u（x） is unknown vector, z = （x₁,x₂,…,x_n） Ω Rz,m≥1,|S₁|issuperficial measure of the unit sphere of RZ, |i|=i₁+ i₂ +… + i., △m=△(△m-1). ,（Ω）, ,（Ω）, … denote the classes of vectors or matrices whose elements belong to L,（Ω）,W,（Ω）,…. A vector or a matrix is said to be continuous differentiable, bounded and measurable if so are its ele-