Renormalized solutions of elliptic equations with general measure data

We study existence and (in some case) uniqueness for elliptic equations with measure data

Nonexistence of solutions for some nonlinear elliptic equations involving measures

Let us recall the following result due to H. Brezis (see [12]). Theorem 1.1 Let Ω be a bounded open subset of RN, N> 2, with 0 ∈ Ω, let f be a function in L1(Ω), and let {fn} be a sequence of L∞(Ω) functions such tha

Orlicz capacities and applications to some existence questions for elliptic PDES having measure data

We study the sequence u(n), which is solution of -div(a(x, del u(n))) + Phi" (\u(n)\) u(n) = f(n) + g(n) in Omega an open bounded set of R-N and u(n) = 0 on partial derivativeOmega, when f(n) tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N-function Phi, and prove a non-existence result

Nonlinear reinforcement problems with right-hand side in L1L^1

We study the asymptotic behaviour, of the entropy solution to a class of nonlinear ``reinforcement problems" and we find the "limit problem"

Definition and existence of renormalized solutions of elliptic equations with general measure data

We introduce a new definition of solution for the nonlinear monotone elliptic problem -div(a(cursive Greek chi, 07u)) = \u3bc in \u3a9, u = 0 on 02\u3a9, where \u3bc is a Radon measure with bounded variation on \u3a9. We prove the existence of such a solution, a stability result, and partial uniqueness results