Best possible estimates of weak solutions of boundary value problems for quasi-linear elliptic equations in unbounded domains

Abstract

We investigate the behaviour of weak solutions of boundary value problems for quasi-linear elliptic divergence second order equations in unbounded domains. We show the boundedness of weak solutions to our problem. Using barrier function and applying the comparison principle, we find the exact exponent of weak solutions decreasing rate near the infinity.

Keywords

• elliptic divergence quasi-linear equations
• weak solutions
• unbounded do- mains
• comparison principle
• barrier function
• primary 35d30
• 35j25
• 35j62
• secondary 35a23
• 35b40
• 35b45
• 35b51