The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations

Abstract

Under the appropriate conditions on u, the generalized solution of the elliptic equation ∫_G {∇v ⋅ A(x, u, ∇u) + vB(x, u, ∇u)}dx = 0, \quad ∀v ∈ {\WW}¹_p(G) ∩ L_∞(G) for which even the natural growth condition p(1 - 1/p^∗) < ϒ < p is permitted, the local and global boundedness of u are proved.