共查询到20条相似文献,搜索用时 31 毫秒
1.
Martin Fuchs 《manuscripta mathematica》1991,72(1):131-140
Given a smooth domain Ω in ℝ
m+1 with compact closure and a smooth integrable functionh: ℝ
m+1→ℝ satisfyingh(x)≥H
∂Ω
(x) on ∂Ω whereH
∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ
m+1 with the properties
andH
∂A=h on ∂A. 相似文献
2.
In this paper, we prove the following theorem regarding the Wang–Yau quasi-local energy of a spacelike two-surface in a spacetime:
Let Σ be a boundary component of some compact, time-symmetric, spacelike hypersurface Ω in a time-oriented spacetime N satisfying the dominant energy condition. Suppose the induced metric on Σ has positive Gaussian curvature and all boundary
components of Ω have positive mean curvature. Suppose H ≤ H
0 where H is the mean curvature of Σ in Ω and H
0 is the mean curvature of Σ when isometrically embedded in
\mathbb R3{\mathbb R^3} . If Ω is not isometric to a domain in
\mathbb R3{\mathbb R^3}, then
1. |
the Brown–York mass of Σ in Ω is a strict local minimum of the Wang–Yau quasi-local energy of Σ. 相似文献
3.
Julián Fernández Bonder Pablo Groisman Julio D. Rossi 《Annali di Matematica Pura ed Applicata》2007,186(2):341-358
The best Sobolev trace constant is given by the first eigenvalue of a Steklov-like problem. We deal with minimizers of the
Rayleigh quotient ‖u‖2
H
1
(Ω)
2/‖u‖2
L
2
(∂Ω) for functions that vanish in a subset A⊂ Ω, which we call the hole. We look for holes that minimize the best Sobolev trace constant among subsets of Ω with prescribed
volume. First, we find a formula for the first variation of the first eigenvalue with respect to the hole. As a consequence
of this formula, we prove that when Ω is a ball the symmetric hole (a centered ball) is critical when we consider deformations
that preserves volume but is not optimal. Finally, we prove that by the Finite Element Method we can approximate the optimal
configuration and, by means of the shape derivative, we design an algorithm to compute the discrete optimal holes.
Mathematics Subject Classification (2000) 35P15, 49K20, 49M25, 49Q10 相似文献
4.
We are concerned with the existence of radial solutions for the following Neumann problem
5.
David Kalaj 《Mathematische Zeitschrift》2008,260(2):237-252
Let Ω and Ω1 be Jordan domains, let μ ∈ (0, 1], and let be a harmonic homeomorphism. The object of the paper is to prove the following results: (a) If f is q.c. and ∂Ω, ∂Ω1 ∈ C
1,μ
, then f is Lipschitz; (b) if f is q.c., ∂Ω, ∂Ω1 ∈ C
1,μ
and Ω1 is convex, then f is bi-Lipschitz; and (c) if Ω is the unit disk, Ω1 is convex, and ∂Ω1 ∈ C
1,μ
, then f is quasiconformal if and only if its boundary function is bi-Lipschitz and the Hilbert transform of its derivative is in
L
∞. These extend the results of Pavlović (Ann. Acad. Sci. Fenn. 27:365–372, 2002).
相似文献
6.
Let be a parametric variational double integral and γ ⊂ ℝ
n
be a system of several distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers
of spanned in γ by solving the Douglas problem for parametric functionals on multiply connected schlicht domains. As a by-product
we obtain a simple isoperimetric inequality for multiply connected -minimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau
problem.
Received: 19 April 2002
Mathematics Subject Classification (2000): 49J45, 49Q10, 53A07, 53A10 相似文献
7.
J. García-Melián C. Morales-Rodrigo J. D. Rossi A. Suárez 《Annali di Matematica Pura ed Applicata》2008,187(3):459-486
In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions
to the semilinear elliptic equation − Δu = λ u − u
p
in Ω, with the nonlinear boundary condition ∂u/∂ν = u
r
on ∂Ω. Here Ω is a smooth bounded domain of with outward unit normal ν, λ is a real parameter and p, r > 0. We also give the precise behavior of solutions for large |λ| in the cases where they exist. The proofs are mainly
based on bifurcation techniques, sub-supersolutions and variational methods.
相似文献
8.
Given an open bounded connected subset Ω of ℝn, we consider the overdetermined boundary value problem obtained by adding both zero Dirichlet and constant Neumann boundary
data to the elliptic equation −div(A(|∇u|)∇u)=1 in Ω. We prove that, if this problem admits a solution in a suitable weak sense, then Ω is a ball. This is obtained under
fairly general assumptions on Ω and A. In particular, A may be degenerate and no growth condition is required. Our method of proof is quite simple. It relies on a maximum principle
for a suitable P-function, combined with some geometric arguments involving the mean curvature of ∂Ω. 相似文献
9.
For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on S = Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l. 相似文献
10.
Pierre Ghienne 《manuscripta mathematica》2002,107(3):289-310
Zabrodsky exact sequences are algebraic tools which express the genus set of a space X in term of its self-maps, when X has the rational homotopy type of a co-ℋ-space or an ℋ-space. Explicit examples show these methods can't be generalized to
the class of all simply connected finite CW-complexes.
We however construct a Zabrodsky exact sequence for those three cells CW-complexes rationally equivalent to the product of
two spheres S
k
×S
n
, n>k≥2. We deduce, from results of Morisugi-Oshima, the genus of some spherical bundles.
Received: 17 March 2001 / Revised version: 8 August 2001 相似文献
11.
Fedor V. Fomin 《Graphs and Combinatorics》2003,19(1):91-99
We prove that for every 2-connected planar graph the pathwidth of its geometric dual is less than the pathwidth of its line
graph. This implies that pathwidth(H)≤ pathwidth(H
*)+1 for every planar triangulation H and leads us to a conjecture that pathwidth(G)≤pathwidth(G
*)+1 for every 2-connected graph G.
Received: May 8, 2001 Final version received: March 26, 2002
RID="*"
ID="*" I acknowledge support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies)
and support by the RFBR grant N01-01-00235.
Acknowledgments. I am grateful to Petr Golovach, Roland Opfer and anonymous referee for their useful comments and suggestions. 相似文献
12.
Morteza Moniri 《Archive for Mathematical Logic》2002,41(1):101-105
For a classical theory T, ℋ(T) denotes the intuitionistic theory of T-normal (i.e. locally T) Kripke structures. S. Buss has asked for a characterization of the theories in the range of ℋ and raised the particular
question of whether HA is an ℋ-theory. We show that T
i
∈ range(ℋ) iff T
i
= ℋ(T). As a corollary, no fragment of HA extending iΠ
1 belongs to the range of ℋ. A. Visser has already proved that HA is not in the range of H by different methods. We provide more examples of theories not in the range of ℋ. We show PA-normality of once-branching Kripke models of HA + MP, where it is not known whether the same holds if MP is dropped.
Received: 15 August 1999 / Published online: 3 October 2001 相似文献
13.
Dian K. Palagachev 《Journal of Global Optimization》2008,40(1-3):305-318
We derive W
2,p
(Ω)-a priori estimates with arbitrary
p ∈(1, ∞), for the solutions of a degenerate oblique derivative problem for linear uniformly elliptic operators with low regular
coefficients. The boundary operator is given in terms of directional derivative with respect to a vector field ℓ that is tangent
to ∂Ω at the points of a non-empty set ε ⊂ ∂Ω and is of emergent type on ∂Ω.
相似文献
14.
Let Ω⊂ℝN be a smooth bounded domain. We characterize smooth vector fields g on ∂Ω which annihilate all harmonic vector fields f in
Ω continuous up to ∂Ω, with respect to the pairing
(dσ denotes the hypersurface measure on ∂Ω). In addition, we extend these results to differential forms with harmonic vector
fields being replaced by harmonic fields, i.e., forms f satisfying df=0, δf=0. A smooth form g on ∂Ω is an annihilator if
and only if suitable extensions, u and v, into Ω of its normal and tangential components on ∂Ω, satisfy the generalized Cauchy-Riemann
system du=δv, δu=0, dv=0 in Ω. Finally, we prove that the described smooth annihilators are weak* dense among all annihilators. Bibliography: 12 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 90–108. 相似文献
15.
Bao Fu Wang 《数学学报(英文版)》2009,25(8):1353-1362
Given a bounded convex domain Ω with C∞ boundary and a function ψ∈C∞(δΩ), Li-Simon-Chen can construct an Euclidean complete and W-complete convex hypersurface M with constant affine Gauss-Kronecker curvature, and they guess the M is also affine complete. In this paper, we give a confirmation answer. 相似文献
16.
Olivier Guibé 《Annali di Matematica Pura ed Applicata》2002,180(4):441-449
We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem -div(a(x,Du))=μ in Ω, u=0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω.
Received: December 27, 2000 Published online: December 19, 2001 相似文献
17.
In this paper, we study the asymptotic behavior of the solutionsu
ε (ε is a small parameter) of boundaryvalue problems for the heat equation in the domain Ωε=Ω−∪Ω
ε
+
∪γ one part of which (Ω
ε
+
) contains ε-periodically situated channels with diameters of order ε and the other part of which (Ω+) is a homogeneous medium; γ=∂Ω
ε
+
∩∂Ω+. On the boundary of the channels the Neumann boundary condition is posed, and on ∂Ωε∩∂Ω the Dirichlet boundary condition is prescribed. The homogenized problem is the Dirichlet problem in Ω with the transmission
condition on γ. The estimates for the difference betweenu
ε and the solution of the homogenized problem are obtained. Bibliography: 14 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 20, pp. 27–47, 1997. 相似文献
18.
In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” uf (·, T) is studied, where uf (x,t) is the solution of the initial boundary-value problem utt−Δu=0 in Ω×(0,T), u|t<0=0, u|∂Ω×(0,T)=f, and the (singular) control f runs over the class L2((0,T); H−m (∂Ω)) (m>0). The following result is established. Let ΩT={x ∈ Ω : dist(x, ∂Ω)<T)} be a subdomain of Ω ⊂ ℝn (diam Ω<∞) filled with waves by a final instant of time t=T, let T*=inf{T : ΩT=Ω} be the time of filling the whole domain Ω. We introduce the notation Dm=Dom((−Δ)m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H2(Ω)∩H
0
1
(Ω);D−m=(Dm)′;D−m(ΩT)={y∈D−m:supp y ⋐ ΩT. If T<T., then the reachable set R
m
T
={ut(·, T): f ∈ L2((0,T), H−m (∂Ω))} (∀m>0), which is dense in D−m(ΩT), does not contain the class C
0
∞
(ΩT). Examples of a ∈ C
0
∞
, a ∈ R
m
T
, are presented.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 7–21.
Translated by T. N. Surkova. 相似文献
19.
V. I. Burenkov M. Lanza de Cristoforis 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):68-89
We consider the Robin Laplacian in two bounded regions Ω1 and Ω2 of ℝ
N
with Lipschitz boundaries and such that Ω2 ⊂ Ω1, and we obtain two-sided estimates for the eigenvalues λ
n,2 of the Robin Laplacian in Ω2 via the eigenvalues λ
n, 1 of the Robin Laplacian in Ω1. Our estimates depend on the measure of the set difference Ω\Ω2 and on suitably defined characteristics of vicinity of the boundaries ∂Ω1 and ∂Ω2, and of the functions defined on ∂Ω1 and on ∂Ω2 that enter the Robin boundary conditions. 相似文献
20.
It is proved that the Stokes operator on a bounded domain, an exterior domain, or a perturbed half-space Ω admits a bounded
H
∞
-calculus on L
q
(Ω) if q(1,∞).
Received: 25 January 2002; in final form: 2 October 2002 /
Published online: 16 May 2003 相似文献
|