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1.
Thomas Schmidt 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):109-129
We consider multi-dimensional variational integrals
where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial -regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring’s lemma, and establishes partial regularity with the optimal H?lder exponent
α in a single step.
相似文献
2.
For finite rank free abelian groups with the standard presentation, the averaged Dehn function is proved to be subquadratic. 相似文献
3.
We consider strictly convex energy densities f: (x) under nonstandard growth conditions. More precisely, we assume that for some constants , and for all Z, Y
n
the inequality
holds with exponents and q< 1. If u denotes a bounded local minimizer of the energy f(w)dx subject to a constraint of the form w a.e. with a given obstacle C1, (), then we prove the local C
1,-regularity of u provided that q < 4 — . This result substantially improves what is known up to now even for the case of unconstrained local minimizers. Bibliography: 27 titles. 相似文献
4.
研究定义在向量u=(u~1,…,u~N):Ω■R~n→R~N上的各项异性积分泛函F(u)=∫_Ωf(x,Du(x))dx和非线性椭圆型方程组-Σi=1nDi(aiα(x,Du(x)))=-Σi=1nDiFiα(x),α=1,2,…,N.在密度函数f:Ω×R~(N×n)→R和矩阵a=(a_i~α):Ω×R~(N×n)→R~(N×n)满足某单调不等式条件下,得到u整体有界. 相似文献
5.
The main result of this paper is an algorithm for approximate matching of a regular expression of size m in a text of size n in time O(nm/logd+2n), where d is the number of allowed errors. This algorithm is the first o(mn) algorithm for approximate matching to regular expressions. 相似文献
6.
7.
Stephen C. Preston 《偏微分方程通讯》2013,38(11):2007-2020
8.
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
9.
Consider the minimization problem
in which
is a normal integrand. Define the convex function
by
It is known that, if the essential domain H of G is open, then problem (P) has a minimizer for any pair of endpoints (u
0, u
1). In this paper, the same result is proved under the condition that, for every point p in H, the subgradient set G(p) is either bounded or empty (when H is open, this condition holds automatically). 相似文献
10.
Summary In this paper we study blow up of the equation
, where
is a two-dimensional white noise field and where Dirichlet boundary conditions are enforced. It is known that if <3/2, then the solution exists for all time; in this paper we show that if is much larger than 3/2, then the solution blows up in finite time with positive probability. We prove this by considering how peaks in the solution propagate. If a peak of high mass forms, we rescale the equation and divide the mass of the peak into a collection of peaks of smaller mass, and these peaks evolve almost independently. In this way we compare the evolution ofu to a branching process. Large peaks are regarded as particles in this branching process. Offspring are peaks which are higher by some factor. We show that the expected number of offspring is greater than one when is much larger than 3/2, and thus the branching process survives with positive probability, corresponding to blowup in finite time.Supported by NSF grant DMS-9021508, NSA grant MDA904-910-H-0034, and ARO Grant MSI DAAL03-91-C-0027Supported by ONR grant N00014-91-J-1526. 相似文献
11.
Xavier Tolsa 《Geometric And Functional Analysis》2007,17(2):605-643
We show that if μ is a finite Borel measure on the complex plane such that
for μ-a.e.
, then μ must be the addition of some point masses, plus some measure absolutely continuous with respect to arc length on countably
many rectifiable curves, plus another measure with zero linear density. We also prove that the same conclusion holds if instead
of the condition
μ-a.e. one assumes
as
-a.e.
Partially supported by grants MTM2004-00519 and Acción Integrada HF2004-0208 (Spain), and 2001-SGR-00431 (Generalitat de Catalunya).
Received: July 2005 Accepted: October 2005 相似文献
12.
该文研究了关于梯度具有次二次增长条件,右端项在L^1空间的一类拟线性椭圆型方程熵解的存在性. 相似文献
13.
Lei Zhu & Faxing Wang 《偏微分方程(英文版)》2015,28(1):23-29
In this paper, we give a new blowup criteria of strong solutions to the Oldroyd model for ideal viscoelastic flow. 相似文献
14.
M. A. Noor K. I. Noor E. Al-Said 《Journal of Optimization Theory and Applications》2011,149(2):441-445
In this paper, we use the auxiliary principle technique to suggest and analyze an implicit iterative method for solving bifunction variational inequalities. We also study the convergence criteria of this new method under pseudomonotonicity condition. 相似文献
15.
Manwai Yuen 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1465-1470
In this paper, we study the blowup of the N-dim Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. We provide a novel integration method to show that the non-trivial classical solutions (ρ,V), with compact support in [0,R], where R>0 is a positive constant and in the sense which ρ(t,r)=0 and V(t,r)=0 for r≥R, under the initial condition
(1) 相似文献
16.
《纯数学与应用数学通讯》2018,71(9):1850-1937
We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite‐time blowup solution with an isolated characteristic blowup point at the origin and a blowup surface that is centered at the origin and has the shape of a stylized pyramid, whose edges follow the bisectrices of the axes in ℝ2. The blowup surface is differentiable outside the bisectrices. As for the asymptotic behavior in similarity variables, the solution converges to the classical one‐dimensional soliton outside the bisectrices. On the bisectrices outside the origin, it converges (up to a subsequence) to a genuinely two‐dimensional stationary solution, whose existence is a by‐product of the proof. At the origin, it behaves like the sum of four solitons localized on the two axes, with opposite signs for neighbors. This is the first example of a blowup solution with a characteristic point in higher dimensions, showing a really two‐dimensional behavior. Moreover, the points of the bisectrices outside the origin give us the first example of noncharacteristic points where the blowup surface is nondifferentiable. © 2018 Wiley Periodicals, Inc. 相似文献
17.
A Bailey Tree for Integrals 总被引:1,自引:0,他引:1
We introduce the notion of integral Bailey pairs. Using the single-variable elliptic beta integral, we construct an infinite binary tree of identities for elliptic hypergeometric integrals. Two particular sequences of identities are described explicitly. 相似文献
18.
Jianwei Dong 《Applicable analysis》2020,99(4):585-595
ABSTRACTIn this paper, we study the compressible isothermal Euler equations with non-vacuum initial data. First, we prove the property of finite propagation to this Cauchy problem by using local energy estimates. Second, we establish the blowup results of the multi-dimensional case in radial symmetry and the one-dimensional case in non-radial symmetry by making assumptions on the initial velocity. Third, we present the blowup results of the three-dimensional case in non-radial symmetry by making assumptions on the initial momentum. 相似文献
19.
Colli Pierluigi Signori Andrea Sprekels Jürgen 《Journal of Optimization Theory and Applications》2022,194(1):25-58
Journal of Optimization Theory and Applications - This paper treats a distributed optimal control problem for a tumor growth model of Cahn–Hilliard type. The evolution of the tumor fraction... 相似文献
20.
考虑二阶非自治弱二次Hamilton系统同宿解的多重性.一般考虑的势函数关于u在无穷远点处的下界函数是一个正常数.而当该系数换为一个正函数而非常数时,情况就会相当不同.该文中讨论了这一问题,将此系数推广到下确界可以是0的一个有关t的正函数.因此该文的结果是对近期一些结果的有意义的改进. 相似文献