Spatial Decay Estimates for a Class of Second-Order Quasilinear Elliptic Partial Differential Equations Arising in Anisotropic Nonlinear Elasticity

Abstract

The spatial decay behavior of solutions of second-order quasilinear elliptic 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-state heat conduction. Differential inequality techniques are employed to obtain exponential decay estimates. The results are illustrated by several examples, one of which is the (isotropic) minimal surface equation. The results are relevant to Saint-Venant principles for nonlinear elasticity as well as to theorems of Phragmen-Lindelof type.