The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations (Journal of Partial Differential Equations, 1991)
Under the appropriate conditions on u, the generalized solution of the elliptic equation &#8747_G {&#8711v &#8901 A(x, u, &#8711u) + vB(x, u, &#8711u)}dx = 0, \quad &#8704v &#8712 {\WW}&sup1_p(G) &#8745 L_&#8734(G) for which even the natural growth condition p(1 - 1/p^&#8727) < &#978 < p is permitted, the local and global boundedness of u are proved.
Keywords: Elliptic equation; critical exponent; natural growth condition; generalized solution; boundedness; H&#246lder continuity