Displaying similar documents to “On a class of semilinear elliptic problems near critical growth.”

The existence of solutions for elliptic systems with nonuniform growth

Y. Q. Fu (2002)

Studia Mathematica

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We study the Dirichlet problems for elliptic partial differential systems with nonuniform growth. By means of the Musielak-Orlicz space theory, we obtain the existence of weak solutions, which generalizes the result of Acerbi and Fusco [1].

Orlicz spaces, α-decreasing functions, and the Δ₂ condition

Gary M. Lieberman (2004)

Colloquium Mathematicae

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We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.

Fine behavior of functions whose gradients are in an Orlicz space

Jan Malý, David Swanson, William P. Ziemer (2009)

Studia Mathematica

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For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.

Musielak-Orlicz-Sobolev spaces on metric measure spaces

Takao Ohno, Tetsu Shimomura (2015)

Czechoslovak Mathematical Journal

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Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness...

Generic existence result for an eigenvalue problem with rapidly growing principal operator

Vy Khoi Le (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the eigenvalue problem - div ( a ( | ∇ u | ) ∇ u ) = λ g ( x , u ) in Ω u = 0 on ∂ Ω , in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all λ > 0 are eigenvalues.