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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.

- CLAUDIA CAPONE, ALBERTO FIORENZA, ANDMIROSLAV KRBEC
- 2006

Yano’s extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator T acting continuously in Lp for p close to 1 and/or taking L∞ into Lp as p→ 1+ and/or p→∞ with norms blowing up at speed (p− 1)−α and/or pβ, α,β > 0. Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens… (More)

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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.

In this paper we prove higher integrability results for vector fields with K ≥ 1 and F ∈ L r (Ω, R n), r > 2 − ε. Applications to the theory of quasiconformal mappings and partial differential equations are given. In particular, we prove regularity results for very weak solutions of equations of the type div a(x, ∇u) = div F. If |a(x, z)| 2 + |z| 2 ≤ (K +… (More)

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)

- Alberto Fiorenza, Anna Mercaldo, Jean-Michel Rakotoson
- Appl. Math. Lett.
- 2001

we extend the results. of [I-5] on the uniqueness of solutions of parabolic equations. Our results give also some regularity results which complete the existence results made in [6-81. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Parabolic equations, Radon measures, Hodge decomposition, Uniqueness, Regularity.

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