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11.
Zhichao Zhang 《Mathematical Methods in the Applied Sciences》2020,43(11):6663-6676
Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the Lp-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given. 相似文献
12.
This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but ) nonlinearities. 相似文献
13.
Connor Mooney 《偏微分方程通讯》2019,44(8):681-690
14.
Areeba Ikram 《Journal of Difference Equations and Applications》2019,25(6):757-775
ABSTRACTWe will establish uniqueness of solutions to boundary value problems involving the nabla Caputo fractional difference under two-point boundary conditions and give an explicit expression for the Green's functions for these problems. Using the Green's functions for specific cases of these boundary value problems, we will then develop Lyapunov inequalities for certain nabla Caputo BVPs. 相似文献
15.
Hüseyin Bor 《Numerical Functional Analysis & Optimization》2019,40(4):484-489
In this article, we prove a general theorem dealing with an application of quasi-f-power increasing sequences and δ-quasi monotone sequences. This theorem also includes some known and new results. 相似文献
16.
Laurent Decreusefond Hélène Halconruy 《Stochastic Processes and their Applications》2019,129(8):2611-2653
On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron–Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of -statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions. 相似文献
17.
Let M be an -dimensional closed orientable submanifold in an -dimensional space form . We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on M defined by , where T is a general symmetric, positive definite and divergence-free -tensor on M. The upper bound is given in terms of an integration involving tr T and , where tr T is the trace of the tensor T and is a normal vector field associated with T and the second fundamental form A of M. Furthermore, we give the sufficient and necessary conditions when the upper bound is attained. Our main theorem can be viewed as an extension of the famous “Reilly inequality”. The operator can be regarded as a natural generalization of the well-known operator which is the linearized operator of the first variation of the -th mean curvature for hypersurfaces in a space form. As applications of our main theorem, we generalize the results of Grosjean [17] and Li–Wang [20] in codimension one to arbitrary codimension. 相似文献
18.
19.
Deguang Zhong Yu Zhou Wenjun Yuan 《Mathematical Methods in the Applied Sciences》2019,42(10):3779-3786
Let be the class of all sense‐preserving homeomorphic self‐mappings of . The aim of this paper is twofold. First, we obtain Heinz‐type inequality for (K,K′)‐quasiconformal mappings satisfying inhomogeneous biharmonic equation Δ(Δω) = g in unit disk with associated boundary value conditions and . Second, we establish biLipschitz continuity for (K,K′)‐quasiconformal mappings satisfying aforementioned inhomogeneous biharmonic equation when and are small enough. 相似文献
20.
We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function with . More precisely, for any we construct -bi-Sobolev maps with identity boundary conditions; for , we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide. 相似文献