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951.
We study the interior and exterior contact problems for hemitropic elastic solids. We treat the cases when the friction effects, described by Tresca friction (given friction model), are taken into consideration either on some part of the boundary of the body or on the whole boundary. We equivalently reduce these problems to a boundary variational inequality with the help of the Steklov–Poincaré type operator. Based on our boundary variational inequality approach we prove existence and uniqueness theorems for weak solutions. We prove that the solutions continuously depend on the data of the original problem and on the friction coefficient. For the interior problem, necessary and sufficient conditions of solvability are established when friction is taken into consideration on the whole boundary. 相似文献
952.
George A. Anastassiou 《Applicable analysis》2013,92(5):993-1017
Here we derive very general multivariate tight integral inequalities of Chebyshev–Grüss, Ostrowski types and of comparison of integral means. These are based on well-known Sobolev integral representation of a function. Our inequalities engage ordinary and weak partial derivatives of the involved functions. We also give their applications. On the way to prove our main results we derive important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. Our results expand to all possible directions. 相似文献
953.
954.
955.
Christopher C. Tisdell 《Journal of Difference Equations and Applications》2013,19(10):1773-1777
This work investigates a two-point boundary value problem (BVP) involving a first-order difference equation, known as the ‘discrete’ BVP. Some sufficient conditions are formulated under which the discrete BVP will possess a unique solution. The innovation herein involves a strategic choice of metric and utilization of Hölder's inequality. This approach enables the associated mappings to be contractive, which were previously non-contractive in traditional settings. This consequently enables an improved application of the fixed-point theorem of Stefan Banach by addressing a wider range of problems than those covered by the current literature. A YouTube video presentation by the author designed to complement this work is available at http://www.youtube.com/watch?v=luLuQ1KyXy8. 相似文献
956.
A. Boulkhemair 《偏微分方程通讯》2013,38(9):1439-1447
We give a proof of the Poincaré inequality in W 1, p (Ω) with a constant that is independent of Ω ? , where is a set of uniformly bounded and uniformly Lipschitz domains in ? n . As a byproduct, we obtain the following: The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the domains Ω vary and remain uniformly bounded and uniformly Lipschitz regular. 相似文献
957.
Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on ?D, and non-negative initial condition. We show that these upper bounds are close to being sharp if (i) the Dirichlet-Laplace-Beltrami operator acting in L 2(D) satisfies a strong Hardy inequality with weight δ2, (ii) the initial temperature distribution, and the specific heat of D are given by δ?α and δ?β respectively, where δ is the distance to ?D, and 1 < α <2, 1 < β <2. 相似文献
958.
《偏微分方程通讯》2013,38(4):539-565
Abstract The spectrum of the Schrödinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any local enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also, if the waveguide is bent, eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schrödinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own right. 相似文献
959.
S. Lakshmanan V. Vembarasan P. Balasubramaniam 《Mathematical Methods in the Applied Sciences》2013,36(4):395-412
This paper investigates the state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. On the basis of the new Lyapunov–Krasovskii functional, some inequality techniques, stochastic stability theory and delay‐dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
960.
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary. 相似文献