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101.
In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems. 相似文献
102.
We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor. 相似文献
103.
Shutao Zhang & Yazhou Han 《分析论及其应用》2022,38(2):178-203
For conformal Hardy-Littlewood-Sobolev(HLS) inequalities [22] and reversed conformal HLS inequalities [8] on $\mathbb{S}^n,$ a new proof is given for the attainability
of their sharp constants. Classical methods used in [22] and [8] depends on rearrangement inequalities. Here, we use the subcritical approach to construct the extremal
sequence and circumvent the blow-up phenomenon by renormalization method. The
merit of the method is that it does not rely on rearrangement inequalities. 相似文献
104.
In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc. 相似文献
105.
Ferenc Mó ricz Ká roly Tandori 《Proceedings of the American Mathematical Society》1996,124(3):877-885
We study the a.e. convergence of orthogonal series defined over a general measure space. We give sufficient conditions which contain the Menshov-Rademacher theorem as an endpoint case. These conditions turn out to be necessary in the particular case where the measure space is the unit interval and the moduli of the coefficients form a nonincreasing sequence. We also prove a new version of the Menshov-Rademacher inequality.
106.
107.
Best possibility of the Furuta inequality 总被引:5,自引:0,他引:5
Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but .
108.
Lai Qinsheng 《Proceedings of the American Mathematical Society》1996,124(2):527-537
Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.
109.
Takayuki Furuta 《Proceedings of the American Mathematical Society》1996,124(10):3071-3075
We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.
110.
Jong-Shi Pang 《Mathematical Programming》1993,58(1-3):149-160
This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968. 相似文献