On Nonlinear Elliptic Equations with General Growth Conditions and L Data

∫ Ω a(∇u) · ∇u dx = ∫ Ω fu dx and − diva(∇u) = f in D′(Ω). Moreover, for all f ∈ L(Ω) there exists a solution of (1.4). It seems natural to define a generalized solution of the problem (1.1), (1.2) for f ∈ L(Ω) as a limit of “variational solutions” and then find some suitable equivalent representation of this limit solution to obtain a larger space for determinig its properties (regularity, uniqueness). Such method is closely related to the abstract theory developed in [3] (see also [4]). WDS'05 Proceedings of Contributed Papers, Part I, 95–101, 2005. ISBN 80-86732-59-2 © MATFYZPRESS