Maximum principles for a fourth order equation from thin plate theory

This paper focuses on a nonlinear equation from thin plate theory of the form Δ (D (x) Δ w) - (1 - ν) [D, w] + c (x) f (w) = 0. We obtain maximum principles for certain functions defined on the solution of this equation using P-functions or auxiliary functions of the types used by Payne [L.E. Payne, Some remarks on maximum principles, J. Anal. Math. 30 (1976) 421-433] and Schaefer [P.W. Schaefer, Solution, gradient, and laplacian bounds in some nonlinear fourth order elliptic equations, SIAM J. Math. Anal. 18 (1987) 430-434].