Nonlocal Variational Principles with Variable Growth
Keyword(s):
This paper is concerned with the functionalJdefined byJ(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, whereΩ⊂ℝNis a regular open bounded set andWis a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation ofJ.
2006 ◽
Vol 36
(0)
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pp. 79-94
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2011 ◽
Vol 56
(7-9)
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pp. 715-753
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2021 ◽
Vol 7
(1)
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pp. 50-65
2017 ◽
Vol 3
(1)
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pp. 70-82
2018 ◽
Vol 8
(2)
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pp. 289-308
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