Recent developments on Dirichlet problems with singular convection/drift terms

Prof. Lucio Boccardo

Abstract: In this talk we study existence and properties of weak/distributional solutions of the Dirichlet problems −÷(M(x)∇u)+a(x)u=−÷(uE(x))+f(x), −÷(M(x)∇ψ)+a(x)ψ=E(x)∇ψ+g(x). In particular we present the Calderon-Zygmund-Stampacchia theory, weak maximum principle, nonlinear problems, extra regularity properties if |f (x)|≤Qa(x), |g(x)| ≤ Qa(x), Q ∈ R+.