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| Operator Equations and Duality Mappings in Sobolev Spaces with Variable Exponents |
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Citation： |
Philippe G. CIARLET,George DINCA,Pavel MATEI.Operator Equations and Duality Mappings in Sobolev Spaces with Variable Exponents[J].Chinese Annals of Mathematics B,2013,34(5):639~666 |
| Page view： 1683
Net amount： 1161 |
Authors： |
Philippe G. CIARLET; George DINCA; Pavel MATEI; |
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| Abstract： |
After studying in a previous work the smoothness of the space
UΓ0 = {u ∈ W1,p(·)(Ω); u = 0 on Γ0 ? Γ = ?Ω},
where dΓ ? measΓ0 > 0, with p(·) ∈ C(Ω) and p(x) > 1 for all x ∈ Ω, the authors
study in this paper the strict and uniform convexity as well as some special properties
of duality mappings defined on the same space. The results obtained in this direction
are used for proving existence results for operator equations having the form J?u = Nfu,
where J? is a duality mapping on UΓ0 corresponding to the gauge function ?, and Nf is
the Nemytskij operator generated by a Carath′eodory function f satisfying an appropriate
growth condition ensuring that Nf may be viewed as acting from UΓ0 into its dual. |
Keywords： |
Monotone operators, Smoothness, Strict convexity, Uniform convexity,
Duality mappings, Sobolev spaces with a variable exponent, Nemytskij
operators |
Classification： |
35J60, 35J25, 47F05 |
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