SPATIAL DECAY-ESTIMATES FOR A CLASS OF 2ND-ORDER QUASI-LINEAR ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS ARISING IN ANISOTROPIC NONLINEAR ELASTICITY

The spatial decay behavior of solutions of second-order quasilinear el liptic partial differential equations, in divergence form, defined on a two-dimensional semi-infinite strip, is investigated. Such equations arise in the theory of anti-plane shear deformations for anisotropic nonlinearly elastic solids and also in anisotropic nonlinear steady-st ate heat conduction. Differential inequality techniques are employed t o obtain exponential decay estimates. The results are illustrated by s everal examples, one of which is the (isotropic) minimal surface equat ion. The results are relevant to Saint-Venant principles for nonlinear elasticity as well as to theorems of Phragmen-Lindelof type.