共查询到20条相似文献,搜索用时 15 毫秒
1.
Morgan Pierre 《Calculus of Variations and Partial Differential Equations》2008,31(2):147-166
Let Aut(D) denote the group of biholomorphic diffeormorphisms from the unit disc D onto itself and O(3) the group of orthogonal transformations of the unit sphere S
2. The existence of multiple solutions to the Dirichlet problem for harmonic maps from D into S
2 is related to the symmetries (if any) of the boundary value γ : ∂D → S
2, by invariance of the Dirichlet energy under the action of Aut(D) × O(3). In this paper, we classify the stabilizers in Aut(D) × O(3) of boundary values in H
1/2(S
1, S
2) and . We give two applications to the Dirichlet problem for harmonic maps.
This work was partially supported by the CMLA, Ecole Normale Supérieure de Cachan, Cachan, France. 相似文献
2.
Luís Almeida 《Calculus of Variations and Partial Differential Equations》1995,3(2):193-242
Let be a Riemannian surface and
be a standard sphere, or more generally a Riemannian manifold on which a Lie group,, acts transitively by isometries. We define generalized harmonic maps by extending the notion of weakly harmonic maps in a natural way (motivated by Noether's Theorem), to mapsu W
loc
1,1
(,
). We prove that, under some slight technical restrictions, for 1 <-p < 2, there are generalized harmonic mapsu W
1,p(,
) that are everywhere discontinuous (in particular, this solves an open problem proposed by F. Bethuel, H. Brezis and F. Hélein, in [BBH]). We also show that the natural -regularity condition for such maps is to require <u to belong to the Lorentz space L(2, ). To prove this -regularity result we extend a compensated compactness result of R. Coifman, P.-L. Lions, Y. Meyer and S. Semmes, proved in [CLMS], to the case of Lorentz spaces in duality. 相似文献
3.
4.
Recently Korevaar and Schoen developed a Sobolev theory for maps from smooth (at least ) manifolds into general metric spaces by proving that the weak limit of appropriate average difference quotients is well
behaved. Here we extend this theory to functions defined over Lipschitz manifold. As an application we then prove an existence
theorem for harmonic maps from Lipschitz manifolds to NPC metric spaces.
Received December 6, 1996 / Accepted March 4, 1997 相似文献
5.
Constructions of harmonic polynomial maps between spheres 总被引:2,自引:0,他引:2
The complexity of
q
-eigenmaps, i.e. homogeneous degreeq harmonic polynomial mapsf:S
m S
n, increases fast with the degreeq and the source dimensionm. Here we introduce a variety of methods of manufacturing new eigenmaps out of old ones. They include degree and source dimension raising operators. As a byproduct, we get estimates on the possible range dimensions of full eigenmaps and obtain a geometric insight of the harmonic product of 2-eigenmaps. 相似文献
6.
Qun Chen 《manuscripta mathematica》1998,95(1):507-517
LetM, N be complete manifolds,u:M →N be a harmonic map with potentialH, namely, a critical point of the functionalE
H
(u)=∫
M
[e(u) − H(u)], wheree(u) is the energy density ofu. We will give a Liouville theorem foru with a class of potentialsH’s.
Research supported in part by NNSFC, SFECC and NSFCCNU. 相似文献
7.
Atsushi Tachikawa 《Calculus of Variations and Partial Differential Equations》2003,16(2):217-224
In this paper, we consider the energy of maps from an Euclidean space into a Finsler space and study the partial regularity of energy minimizing maps. We show that the -dimensional Hausdorff measure of the singular set of every energy minimizing map is 0 for some , when m=3,4.
Received: 6 June 2001 / Accepted: 10 July 2001 / Published online: 12 October 2001 相似文献
8.
Takeshi Isobe 《Journal of Geometric Analysis》1998,8(3):447-463
We study the regularity of harmonic maps from Riemannian manifold into a static Lorentzian manifold. We show that when the
domain manifold is two-dimensional, any weakly harmonic map is smooth. We also show that when dimension n of the domain manifold
is greater than two, there exists a weakly harmonic map for the Dirichlet problem which is smooth except for a closed set
whose (n − 2)-dimensional Hausdorff measure is zero. 相似文献
9.
We consider partial regularity for energy minimizing maps satisfying a partially free boundary condition. This condition takes
the form of the requirement that a relatively open subset of the boundary of the domain manifold be mapped into a closed submanifold
with non-empty boundary, contained in the target manifold. We obtain an optimal estimate on the Hausdorff dimension of the
singular set of such a map. Our result can be interpreted as regularity result for a vector-valued Signorini, or thin-obstacle,
problem. 相似文献
10.
Yuguang Shi You-De Wang 《Calculus of Variations and Partial Differential Equations》2000,10(2):171-196
In this paper we consider the Dirichlet problem at infinity of proper harmonic maps from noncompact complex hyperbolic space
to a rank one symmetric space N of noncompact type with singular boundary data . Under some conditions on f, we show that the Dirichlet problem at infinity admits a harmonic map which assumes the boundary data f continuously.
Received: March 11, 1999 / Accepted April 23, 1999 相似文献
11.
Etienne Sandier Itai Shafrir 《Calculus of Variations and Partial Differential Equations》1994,2(1):113-122
We study the uniqueness of minimizing harmonic maps to a closed hemisphere. We are able to describe the boundary data for which there are more than one minimizer, and to describe in these cases the corresponding set of minimizers. This is a limiting case for a former result of W.Jäger and H.Kaul.This article was processed by the author using the Springer-Verlag TEX PJourlg macro package 1991. 相似文献
12.
Boling Guo Min-Chun Hong 《Calculus of Variations and Partial Differential Equations》1993,1(3):311-334
We prove a global existence of solutions for the Landau-Lifshitz equation of the ferromagnetic spin chain from am-dimensional manifoldM into the unit sphereS
2 of 3 and establish some new links between harmonic maps and the solutions of the Landau-Lifshitz equation. 相似文献
13.
Qun Chen 《manuscripta mathematica》1998,95(4):507-517
Let M, N be complete manifolds, u:M→N be a harmonic map with potential H, namely, a critical point of the functional , where e(u) is the energy density of u. We will give a Liouville theorem for u with a class of potentials H's.
Received: Received: 10 July 1997 相似文献
14.
Sigmundur Gudmundsson 《manuscripta mathematica》1994,85(1):67-78
We give a method for constructing non-holomorphic harmonic morphisms from Kähler manifolds. The method is then used to obtain many such examples defined locally on the complex Grassmannians. 相似文献
15.
In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time approximation of the optimal switching problem, and analyse its rate of convergence. Given a time step h, the error is in general of order (hlog(1/h))1/2, and of order h1/2 when the switching costs do not depend on the state process. We next propose quantization numerical schemes for the space discretization of the discrete-time Euler state process. A Markovian quantization approach relying on the optimal quantization of the normal distribution arising in the Euler scheme is analysed. In the particular case of uncontrolled state process, we describe an alternative marginal quantization method, which extends the recursive algorithm for optimal stopping problems as in Bally (2003) [1]. A priori Lp-error estimates are stated in terms of quantization errors. Finally, some numerical tests are performed for an optimal switching problem with two regimes. 相似文献
16.
Michael Struwe 《manuscripta mathematica》1998,96(4):463-486
Harmonic maps from B
1 (0, ℝ3) to a smooth compact target manifold N with uniformly small scaled energy (see assumption (2) below) are shown to be unique for their boundary values.
Received: 12 May 1997 相似文献
17.
We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold . As a consequence we can construct sequences of H‐surfaces and almost complex surfaces. 相似文献
18.
Summary We consider the harmonic map heat flow from the three-dimensional ball to the two-sphere. We establish the existence of regular initial data leading to blow-up in finite time. 相似文献
19.
This paper is concerned with a trigonometric Hermite wavelet Galerkin method for the Fredholm integral equations with weakly singular kernel. The kernel function of this integral equation considered here includes two parts, a weakly singular kernel part and a smooth kernel part. The approximation estimates for the weakly singular kernel function and the smooth part based on the trigonometric Hermite wavelet constructed by E. Quak [Trigonometric wavelets for Hermite interpolation, Math. Comp. 65 (1996) 683–722] are developed. The use of trigonometric Hermite interpolant wavelets for the discretization leads to a circulant block diagonal symmetrical system matrix. It is shown that we only need to compute and store O(N) entries for the weakly singular kernel representation matrix with dimensions N2 which can reduce the whole computational cost and storage expense. The computational schemes of the resulting matrix elements are provided for the weakly singular kernel function. Furthermore, the convergence analysis is developed for the trigonometric wavelet method in this paper. 相似文献
20.
In this paper, we can prove that any non‐degenerate strongly harmonic map ? from a compact Berwald manifold with nonnegative general Ricci curvature to a Landsberg manifold with non‐positive flag curvature must be totally geodesic, which generalizes the result of Eells and Sampson ([2]). 相似文献