Prior bounds on generalized derivatives of solutions of second-order quasilİnear elliptic equations

Abstract

For the equations λu−dºa(x,u$\nabla$u) = f, λu−f = a(x, u,$\nabla$ u)ºd²u ∀f = Re f ∈ L¹ (Re^l, d^lx) ∩L^∞ (R^lx) ∩ C^∞ (Rⁱ, d^lx) with smooth coefficients in R^l we establish prior bounds on the first and second generalized derivatives of their solutions in the spaces L^2p (R^l, d^lx), L^p(Rl, d^lx), 1 < p < ∞, respectively.