Gradient bounds for weakly coupled nonlinear elliptic systems

摘要

Gradient bounds are established for soultions of weakly coupled nonlinear systems of the formthe functionis shown to satisfy a maximum principle for eachi=0, 1:2,#x2026;,m. The constants #x3B2;,#x3B3; are chosen appropriately andfiis related to the nonlinear coupling termshk,(x,u). In establishing this result, an extension of previous gradient bounds for a single semilinear elliptic equation is obtained, one related to previous work of Payne, Stakgold, Sperb and others.