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Weak solution for obstacle problem with variable growth. (English) Zbl 1064.46022
Summary: In this paper, we introduce the weighted spaces \(L^{p(x)}(\Omega,\omega)\) and \(W^{k,p(x)}(\Omega,\omega)\). After discussing the properties of these spaces, we obtain the existence and uniqueness of weak solutions for obstacle problem with variable growth in the setting of these spaces.

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Full Text: DOI
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