Continuity theorem for nonlinear integral functionals and Aumann-Perles' variational problem (Q1081108)
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scientific article; zbMATH DE number 3969476
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuity theorem for nonlinear integral functionals and Aumann-Perles' variational problem |
scientific article; zbMATH DE number 3969476 |
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Continuity theorem for nonlinear integral functionals and Aumann-Perles' variational problem (English)
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1986
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The paper deals with the problem min\(\int_{T}f(t,u(t))d\mu (t)\) subject to the constraint \(\int_{T}g(t,u(t))d\mu (t)\leq c\). The existence of a solution \(u\in L^ 1(T,\mu)\) is proved by using the standard direct method of the calculus of variations, consisting in proving the weak \(L^ 1(T)\) lower semicontinuity of the functional \(\int_{T}f(t,u(t))d\mu (t)\) and the weak \(L^ 1(T)\) compactness of the constraint \(\int_{T}g(t,u(t))d\mu (t)\leq c\).
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integral functionals
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\(L^ 1\)-weak compactness
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direct method
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lower semicontinuity
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