Interior estimates for solutions of linear elliptic inequalities

摘要

We study the wedge of solutions of the inequality A(u) >= 0, where A is a linear elliptic operator of order 2m acting on functions of n variables. We establish interior estimates of the form parallel to u; w(p)(2m-1) (omega)parallel to <= C(omega, Omega)parallel to U; L(Omega) for the elements of this wedge, where omega is a compact subdomain of Omega, W-p(2m-1) (omega) is the Sobolev space, p(n - 1) < n, L(Omega) is the Lebesgue space of integrable functions, and the constant C(omega, Omega) is independent of u.