MAXIMUM-PRINCIPLES AND A PRIORI ESTIMATES FOR A CLASS OF PROBLEMS FROM NONLINEAR ELASTICITY

We consider smooth solutions, U, to the nonlinear elliptic system associated with a two dimensional elastic material which has energy functional [GRAPHICS] The function H (d) is nonnegative, convex and unbounded in a neighborhood of zero. Two maximum principles are proved for DU and we show that if OMEGA' subset-of subset-of OMEGA then parallel-to DU parallel-to C-alpha(OMEGA') and parallel-to DU-1 parallel-to L infinity (OMEGA') are bounded a priori in terms of parallel-to DU parallel-to L(p)(OMEGA) and W (U) for some p = p (H).