A "nonlinear duality" approach to $ W_0^{1, 1} $ solutions in elliptic systems related to the Keller-Segel model

Abstract

In this paper, we prove existence of distributional solutions of a nonlinear elliptic system, related to the Keller-Segel model. Our starting point is the boundedness theorem (for solutions of elliptic equations) proved by Guido Stampacchia and Neil Trudinger.

Keywords

• duality method
• nonlinear elliptic system
• $ w_0^{1
• 1} $ solutions