Marco Picerni

Existence and regularity of solutions to parabolic–elliptic nonlinear systems

Abstract In this paper, we study the existence and summability of the solutions to the following parabolic–elliptic system of partial differential equations with discontinuous coefficients: $$\begin{aligned} \left\{ \begin{array}{cc} u_t-\operatorname {div}(A(x, t) \nabla u)=-\op...

Mosco-Convergence of Convex Sets and Unilateral Problems for Differential Operators with Lower Order Terms Having Natural Growth

We study the stability of solutions to a class of variational inequalities posed on obstacle-type convex sets, under Mosco-convergence. Specifically, we consider problems of the form {u∈W01,p(Ω)∩L∞(Ω),u≥ψ in Ω,⟨A(u),v−u⟩+∫ΩH(x,u,Du)(v−u)≥0,∀ v∈W01,p(Ω)∩L∞(Ω),v≥ψ in Ω. Here, A is...