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V. G. Osmolovskii 《Journal of Mathematical Sciences》1995,73(6):701-710
We prove the following theorem: Suppose the function f(x) belongs toL q (ω, ? n ), ω ? ? m , q∈(1, ∞), and satisfies the inequality $$|\int\limits_\omega {(f(x),{\mathbf{ }}v(x)){\mathbf{ }}dx| \leqslant \mu ||} v||'_q ,{\mathbf{ }}\tfrac{1}{q} + \tfrac{1}{{q'}} = 1,$$ for all n-dimensional vector-valued functions in the kernel of a scalar-valued first-order differential operator £ for which the second-order operatorLL * is elliptic. Then there exists a function p(x)∈W q 1 (ω) such that $$||f(x) - \mathfrak{L}^* p(x)||q \leqslant C_q \mu .$$ Bibliography: 6 titles. 相似文献
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Translated from Optimal'nost Upravlyaemykh Dinamicheskikh Sistem, Sbornik Trudov VNIISI, No. 14, pp. 76–86, 1990. 相似文献
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Michael Bildhauer Martin Fuchs Victor Osmolovskii 《Mathematical Methods in the Applied Sciences》2002,25(2):149-178
We consider the problem of minimizing among functions u:?d?Ω→?d, u∣?Ω=0, and measurable subsets E of Ω. Here fh+, f? denote quadratic potentials defined on Ω¯×{symmetric d×d matrices}, h is the minimum energy of fh+ and ε(u) is the symmetric gradient of the displacement field u. An equilibrium state û, Ê of J(u,E) is called one‐phase if E=?? or E=Ω, two‐phase otherwise. For two‐phase states, σ∣?E∩Ω∣ measures the effect of the separating surface, and we investigate the way in which the distribution of phases is affected by the choice of the parameters h??, σ>0. Additional results concern the smoothness of two‐phase equilibrium states and the behaviour of inf J(u,E) in the limit σ↓0. Moreover, we discuss the case of additional volume force potentials, and extend the previous results to non‐zero boundary values. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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M. Bildhauer M. Fuchs V. G. Osmolovskii 《Mathematical Methods in the Applied Sciences》2002,25(4):289-308
We consider the problem of minimizing 0<p<1, h∈?, σ>0, among functions u:?d?Ω→?d, u∣?Ω=0, and measurable characteristic functions χ:Ω→?. Here ?+h, ??, denote quadratic potentials defined on the space of all symmetric d×d matrices, h is the minimum energy of ?+h and ε(u) denotes the symmetric gradient of the displacement field. An equilibrium state û, χ?, of I [·,·,h, σ] is termed one‐phase if χ?≡0 or χ?≡1, two‐phase otherwise. We investigate the way in which the distribution of phases is affected by the choice of the parameters h and σ. Copyright 2002 John Wiley & Sons, Ltd. 相似文献
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V. G. Osmolovskii 《Journal of Mathematical Sciences》2006,135(6):3437-3456
All the equilibrium states of a one-dimensional variational phase-transition problem are explicitly found. The temperature-dependence
of the stability of one-phase equilibrium states is studied. Bibliography: 5 titles.
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Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 3–19. 相似文献
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