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Mathematics
Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces
I. V. Orlov, I. A. Romanenko V. I. Vernadsky Crimean Federal University, 4, Vernadskogo ave., 295007, Simferopol, Republic of Crimea, Russia
Abstract:
For variational functionals in Sobolev spaces $\{W^{1,p}\}\;(1\leq p<\infty)$ we introduce a sequence of so-called dominant “growth estimates” for the gradient of appropriate order of the integrand, each of which guarantees the appropriate level of smoothness of variational functional in the $C^{1}$-smooth points of the Sobolev space. Earlier studied K-pseudopolynomial representations of the integrand are particular cases of dominant growth estimates. However, unlike the pseudopolynomial case $(p\in \mathbb{N})$, our approach enables us to consider variational problems on the complete Sobolev scale $(1\leq p<\infty)$.
Key words:
variational functional, Sobolev spaces, integrant, dominant growth estimates, dominating mixed smoothness, variational problems.
Citation:
I. V. Orlov, I. A. Romanenko, “Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces”, Izv. Saratov Univ. Math. Mech. Inform., 15:4 (2015), 422–432
Linking options:
https://www.mathnet.ru/eng/isu610 https://www.mathnet.ru/eng/isu/v15/i4/p422
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Abstract page: | 281 | Full-text PDF : | 78 | References: | 46 |
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