THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS

摘要

In this paper, the first boundary value problem for quasilinear equation of the form ΔA(u, x) + ∑ from i=1 to m of (partial deriv b~i(u, x)/(partial deriv x_i)+ c(u, x) = 0, A_u(u, x) ≥ 0 is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.