Regularizing effects in some elliptic systems with a convection term

In this paper we study existence and summability of positive solutions for the elliptic system {- div((a(x) + u)(rho) del u) + u = - div(u M(x)del psi) + f(x), in Omega, - div(M(x)del psi) = u(lambda) , in Omega. Here rho >= 1 and lambda > 0, while f(x) >= 0 is a function in L-m(Omega), m >= 1. The main feature of the system is that it exhibits a regularizing effect: the solutions are more regular than those of the two equations taken singularly. (c) 2022 Elsevier Inc. All rights reserved.