Maximum principles for a fourth order equation from thin plate theory

AbstractThis paper focuses on a nonlinear equation from thin plate theory of the form Δ(D(x)Δw)−(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]