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An optimal decomposition formula for the norm in the Orlicz space L(log L) α is given. New proofs of some results involving L(log L) α spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes.
We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents… (More)
We study the sequence u n , which is solution of −div(a(x, ∇u n)) + Φ (|u n |) u n = f n + g n in Ω an open bounded set of R N and u n = 0 on ∂Ω, 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 Φ, and prove a non-existence result.