Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range

Robert Černý

Open Mathematics, Tome 12 (2014), p. 114-127 / Harvested from The Polish Digital Mathematics Library

Résumé

Let n ≥ 2 and let Ω ⊂ ℝn be an open set. We prove the boundedness of weak solutions to the problem u∈W01LΦΩand-divΦ'∇u∇u∇u+VxΦ'uuu=fx,u+μhxinΩ, where ϕ is a Young function such that the space W 01 L Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V(x) is a continuous potential, h ∈ L Φ(Ω) is a non-trivial continuous function and µ ≥ 0 is a small parameter. We consider two classical cases: the case of Ω being an open bounded set and the case of Ω = ℝn.

Détail

Publié le : 2014-01-01

Zbl 1287.35029

EUDML-ID : urn:eudml:doc:269606

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