Second-order boundary estimates for large positive solutions to an elliptic system of competitive type

Abstract

In this paper, we study the second-order boundary asymptotic behaviour for large positive solutions to an elliptic system of competitive type. First, we derive a second-order estimate to a related single weighted equation with boundary blow-up data. Then, by relaxing the system and iterating the estimate of the single equation, we establish second-order estimates of the solutions.