共查询到20条相似文献,搜索用时 10 毫秒
1.
Mihai N. Pascu 《Transactions of the American Mathematical Society》2002,354(11):4681-4702
We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.
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We study the fully inhomogeneous Dirichlet problem for the Laplacian in bounded convex domains in Rn, when the size/smoothness of both the data and the solution are measured on scales of Besov and Triebel-Lizorkin spaces. As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates. As a corollary, sharp estimates for the Green potential are obtained in a variety of contexts, including local Hardy spaces. A substantial part of this analysis applies to bounded semiconvex domains (i.e., Lipschitz domains satisfying a uniform exterior ball condition). 相似文献
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Let A be a nonnegative integer matrix, and let e denote the vector all of whose components are equal to 1. The pluperfect graph theorem states that if for all integer vectors b the optimal objective value of the linear program minse′xvbAx ? b, x ? 0 s is integer, then those linear programs possess optimal integer solutions. We strengthen this theorem and show that any lexicomaximal optimal solution to the above linear program (under any arbitrary ordering of the variables) is integral and an extreme point of sxvbAx ? b, x ? 0 s. We note that this extremality property of integer solutions is also shared by covering as well as packing problems defined by a balanced matrix A. 相似文献
5.
S. R. Nasyrov 《Mathematical Notes》2007,82(5-6):798-802
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane. 相似文献
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LetB
1
be a ball of radiusr
1
inS
n
(ℍn), and letB
0
be a smaller ball of radiusr
0
such thatB
0
⊂B
1
. ForS
n
we considerr
1
π. Let u be a solution of the problem- δm = 1 in Ω :=B
1
/B
0
vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian
on Ω is maximal if and only if the balls are concentric. 相似文献
7.
Honghui Yin 《Mathematical Methods in the Applied Sciences》2012,35(3):307-313
In this paper, we study the existence of three solutions to a Neumann problem with nonstandard growth conditions. The technical approach is mainly based on three critical points theorem due to Ricceri. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
In this article, we verify Dade's projective invariant conjecture for the symplectic group Sp4(2 n ) and the special unitary group SU4(22n ) in the defining characteristic, that is, in characteristic 2. Furthermore, we show that the Isaacs–Malle–Navarro version of the McKay conjecture holds for Sp4(2 n ) and SU4(22n ) in the defining characteristic, that is, Sp4(2 n ) and SU4(22n ) are good for the prime 2 in the sense of Isaacs, Malle, and Navarro. 相似文献
9.
Let and Ω be a bounded Lipschitz domain in . Assume that and the function is non-negative, where ?Ω denotes the boundary of Ω. Denote by ν the outward unit normal to ?Ω. In this article, the authors give two necessary and sufficient conditions for the unique solvability of the Robin problem for the Laplace equation in Ω with boundary data , respectively, in terms of a weak reverse Hölder inequality with exponent p or the unique solvability of the Robin problem with boundary data in some weighted space. As applications, the authors obtain the unique solvability of the Robin problem for the Laplace equation in the bounded (semi-)convex domain Ω with boundary data in (weighted) for any given . 相似文献
10.
Xingfei Xiang 《Journal of Mathematical Analysis and Applications》2022,505(2):125518
In bounded convex domains, the regularity of a vector field u with its , in space and the tangential component or the normal component of u over the boundary in space, is established for . As an application, we derive an estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal. 相似文献
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Annette Huber 《Mathematische Nachrichten》2008,281(12):1764-1776
We clarify the expected properties of the slice filtration on triangulated motives from the point of view of the generalized Hodge conjecture. In the appendix, J. Ayoub proves unconditionally that the slice filtration does not respect geometric motives. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
设n,a,b,c是正整数,gcd(a,b,c)=1,a,b≥3,且丢番图方程a~x+b~y=c~z只有正整数解(x,y,z)=(1,1,1).证明了若(x,y,z)是丢番图方程(an)~x+(bn)~y=(cn)~z的正整数解且(x,y,z)≠(1,1,1),则yzz或xzy.还证明了当(a,b,c)=(3,5,8),(5,8,13),(8,13,21),(13,21,34)时,丢番图方程(an)~x+(bn)~y=(cn)~z只有正整数解(x,y,z)=(1,1,1). 相似文献
14.
The purpose of this article is to study a categorification of the n-th tensor power of the spin representation of U(𝔰𝔬(7, ?)) by using certain subcategories and projective functors of the Bernstein–Gelfand–Gelfand (BGG) category of the complex Lie algebra 𝔤𝔩 n . 相似文献
15.
We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain Ω0 of the domain of definition Ω of the energy balance equation and of the Poisson equation. Here Ω0 corresponds to the region of semiconducting material, Ω \ Ω0 represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two‐dimensional stationary energy model. For this purpose we derive a W1,p ‐regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
WEI DaSheng 《中国科学 数学(英文版)》2014,(1)
We determine the sum of two integral squares over imaginary quadratic fields Q(√-2p),where p≡1 mod 8 is a prime satisfying 2p=r2+s2with r,s≡±3 mod 8. 相似文献
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In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed. We study the effect of the use of transformations on the approximation of univariate (convex) functions. In this paper, we show that these transformations can be used to construct upper and lower bounds for nonconvex functions. Moreover, we show that by using such transformations of the input variable or the output variable, we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations. We show that these transformations can be applied to the approximation of a (convex) Pareto curve that is associated with a (convex) bi-objective optimization problem. 相似文献
19.
Ding Guanggui 《数学物理学报(B辑英文版)》2009,29(3)
This is such a article to consider an "into" isometric mapping between two unit spheres of two infinite dimensional spaces of different types.In this article, we find a useful condition (using the Krein-Milman property) under which an into-isometric mapping from extended. 相似文献
20.
V. S. Balaganskii 《Mathematical Notes》2006,79(3-4):299-313
We construct a convex smooth antiproximinal set in any infinite-dimensional space c 0(Γ) equipped with the Day norm; moreover, the distance function to the set is Gâteaux differentiable at each point of the complement. 相似文献