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

Let n ≥ 2 and let Ω ⊂ ℝn be an open set. We prove the boundedness of weak solutions to the problem uW01LΦΩand-divΦ'uuu+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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:269606
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     author = {Robert \v Cern\'y},
     title = {Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {114-127},
     zbl = {1287.35029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0329-2}
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Robert Černý. Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range. Open Mathematics, Tome 12 (2014) pp. 114-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0329-2/

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