Theorems on Lower Semicontinuity and Relaxation for Integrands with Fast Growth |
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Authors: | M A Sychev |
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Institution: | (1) Sobolev Institute of Mathematics, Novosibirsk, Russia |
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Abstract: | We prove theorems on the lower semicontinuity and integral representations of the lower semicontinuous envelopes of integral functionals with integrands L of fast growth: c
1
G(|Du|) + c
2 L c
3
G(|Du|) + c
4 with c
3 c
1 > 0 and G : 0, 0, is an increasing convex function such that vG (v)/G(v) as v and is increasing for large v. Repeating the results for the case of the standard growth (G() = ||p) the quasiconvexity of integrands characterizes the lower semicontinuity of integral functionals and their quasiconvexifications yield the integral functionals that are lower semicontinuous envelopes.Original Russian Text Copyright © 2005 Sychev M. A.The author was supported by the Russian Foundation for Basic Research (Grant 03-01-00162).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 679–697, May–June, 2005. |
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Keywords: | Young measures lower semicontinuity lower semicontinuous envelopes integrands with fast growth quasiconvexity |
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