共查询到20条相似文献,搜索用时 15 毫秒
1.
On the Existence of Extremals for the Sobolev Trace Embedding Theorem with Critical Exponent 总被引:3,自引:0,他引:3
In this paper, the existence problem is studied for extremalsof the Sobolev trace inequality W1,p()Lp*(), where is a boundedsmooth domain in RN, p*=p(N1)/(Np), is the criticalSobolev exponent, and 1 < p < N. 2000 Mathematics SubjectClassification 35J65 (primary), 35B33 (secondary). 相似文献
2.
A. I. Nazarov 《Journal of Mathematical Sciences》2001,107(3):3841-3859
Varying conditions on the weight function f, the author is interested in whether the extremal of the ratio $\inf \frac{{\left\| {\nabla u} \right\|_{Lp} \left( \Omega \right)}}{{\left\| {fu} \right\|_{Lp} \left( \Omega \right)}}{\lambda }_{pq} \left( {\Omega ,f} \right)$ remains symmetric. Here, f is positive almost everywhere in $u \in \mathop {W_p^1 }\limits^{\text{O}} \left( \Omega \right)$ and the infimum is taken over all functions $u \in \mathop {W_p^1 \left( \Omega \right)}\limits^{\text{O}}$ . Bibliography: 23 titles. 相似文献
3.
This paper offers a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on R~n. The authors use this idea to extend the result to real hyperbolic spaces H~n. 相似文献
4.
Amos Uderzo 《Set-Valued and Variational Analysis》2009,17(4):409-430
Some properties, connected with recent generalizations of the classic notion of Lipschitz continuity for multifunctions, are
investigated with reference to variational systems, that is to solution maps associated to parametrized generalized equations.
The latter ones are a convenient framework to address several questions, mainly related to the stability and sensitivity analysis,
arising in mathematical programming, optimal control, equilibrium and variational inequality theory. Global and local criteria
for metric regularity and Lipschitz-likeness of variational systems are obtained. Some applications to the exact penalization
of mathematical programs with equilibrium constraints and to the Lipschitzian stability of fixed points for multivalued contractions
are then considered. 相似文献
5.
Yoichi Miyazaki 《Milan Journal of Mathematics》2014,82(2):297-312
We give a direct and elementary proof for the trace theorem in L p -based Sobolev spaces, when the domain is the unit disk. We also consider the Dirichlet boundary problem for the Laplace equation, where the boundary value is a function in the Besov space. The Poisson kernel enables us to solve this problem in the unit disk more easily than in a general domain. 相似文献
6.
We prove that the Sobolev embedding operator S
d,k,p :
, where 1/s=1/p-k/d , is (v,1) -absolutely summing for appropriate v > 1 . The result is optimal for s
2 . 相似文献
7.
M. Bildhauer 《Journal of Mathematical Sciences》2003,115(6):2747-2752
Uniqueness is proved for solutions of the dual problem that is associated with the minimum problem
among the mappings
with prescribed Dirichlet boundary data and for smooth strictly convex integrands f of linear growth. No further assumptions on f or its conjugate function
are imposed, in particular,
is not assumed to be strictly convex. A special solution of the dual problem is seen to be a mapping into the image of
, which immediately implies uniqueness. Bibliography: 13 titles. 相似文献
8.
本文从推导非双射变换可以作成一个半群出发,论证了任何半群和变换半群的关系,并推出了半群的广义结合律和广义交换律. 相似文献
9.
Mathematical Notes - Properties of functions from the Sobolev orthogonal system $$mathfrak{W}_{r}$$ generated by the Walsh system are studied. In particular, recurrence relations for functions... 相似文献
10.
11.
We discuss here generalized proximal point methods applied to variational inequality problems. These methods differ from the classical point method in that a so-called Bregman distance substitutes for the Euclidean distance and forces the sequence generated by the algorithm to remain in the interior of the feasible region, assumed to be nonempty. We consider here the case in which this region is a polyhedron (which includes linear and nonlinear programming, monotone linear complementarity problems, and also certain nonlinear complementarity problems), and present two alternatives to deal with linear equality constraints. We prove that the sequences generated by any of these alternatives, which in general are different, converge to the same point, namely the solution of the problem which is closest, in the sense of the Bregman distance, to the initial iterate, for a certain class of operators. This class consists essentially of point-to-point and differentiable operators such that their Jacobian matrices are positive semidefinite (not necessarily symmetric) and their kernels are constant in the feasible region and invariant through symmetrization. For these operators, the solution set of the problem is also a polyhedron. Thus, we extend a previous similar result which covered only linear operators with symmetric and positive-semidefinite matrices. 相似文献
12.
We study a linear four-element equation in the class of solutions that are holomorphic outside an isosceles trapezium and vanish at infinity. The equation is used here to investigate the Hamburger moments problem for entire functions of exponential type. 相似文献
13.
一个模嵌入自由模相当于用坐标来表示元素,这在数学上一直有重要意义.理论上, QF-环上的模都可以嵌入自由模,但没有好的算法,影响了它的应用.本文给出QF-环上有限生成模的最小嵌入的一种算法和所嵌入自由模的秩数的估计. 相似文献
14.
Julián Fernández Bonder Nicolas Saintier Analia Silva 《Annali di Matematica Pura ed Applicata》2014,193(6):1607-1628
In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions and therefore to ensure the existence of extremals. 相似文献
15.
16.
Let H2(γ) be the Hilbert space over the bidisk D2 generated by a positive sequence γ={γnm}n,m ≥ 0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H2(γ) with γ={γnm}n,m ≥ 0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D2. 相似文献
17.
18.
Seongchan Kim 《Regular and Chaotic Dynamics》2018,23(3):304-324
In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body. 相似文献
20.
Functional Analysis and Its Applications - We consider the problem of the constancy of the minimizer in the fractional embedding theorem $$mathcal{H}^s(Omega) hookrightarrow L_q(Omega)$$ for a... 相似文献