Gradient bounds for weakly coupled nonlinear elliptic systems

Abstract

Gradient bounds are established for soultions of weakly coupled nonlinear systems of the form

the function

is shown to satisfy a maximum principle for each i=0, 1:2,…,m. The constants β,γ are chosen appropriately and f _i is related to the nonlinear coupling terms h _k ,(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.

AMS(MOS):

• No.35J60

^†Supported in part by NSF Grant No. MCS 81-00801.

^‡Supported in part by NSF Grant No. MCS 79-05791.

^†Supported in part by NSF Grant No. MCS 81-00801.

^‡Supported in part by NSF Grant No. MCS 79-05791.

Notes

^†Supported in part by NSF Grant No. MCS 81-00801.

^‡Supported in part by NSF Grant No. MCS 79-05791.