共查询到20条相似文献,搜索用时 10 毫秒
1.
Séverine Rigot 《Calculus of Variations and Partial Differential Equations》2000,10(4):389-406
Quasi minimizers for the perimeter are measurable subsets G of such that
for all variations of G with and for a given increasing function such that . We prove here that, given , G a reduced quasi minimizer, and , there are , with , and , homeomorphic to a closed ball with radius t in , such that for some absolute constant . The constant above depends only on n, and . If moreover for some , we prove that we can find such a ball such that is a dimensional graph of class . This will be obtained proving that a quasi minimizer is equivalent to some set which satisfies the condition B. This condition
gives some kind of uniform control on the flatness of the boundary and then criterions proven by Ambrosio-Paolini and Tamanini
can be applied to get the required regularity properties.
Received: July 12, 1999 / Accepted: October 1, 1999 相似文献
2.
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
3.
Martin Svensson 《manuscripta mathematica》2002,107(1):1-13
We study holomorphic harmonic morphisms from K?hler manifolds to almost Hermitian manifolds. When the codomain is also K?hler
we get restrictions on such maps in the case of constant holomorphic curvature. We also prove a Bochner-type formula for holomorphic
harmonic morphisms which, under certain curvature conditions of the domain, gives insight to the structure of the vertical
distribution. We thus prove that when the domain is compact and non-negatively curved, the vertical distribution is totally
geodesic.
Received: 28 May 2001 相似文献
4.
5.
Annalisa Baldi Bruno Franchi 《Calculus of Variations and Partial Differential Equations》2003,16(3):283-298
Abstract. In this paper we study the notion of perimeter associated with doubling metric measures or strongly weights. We prove that the metric perimeter in the sense of L. Ambrosio and M. Miranda jr. coincides with the metric Minkowski
content and can be obtained also as a -limit of Modica-Mortola type degenerate integral functionals.
Received: 27 August 2001 / Accepted: 29 November 2001 / Published online: 10 June 2002
Investigation supported by University of Bologna, funds for selected research topics and by GNAMPA of INdAM, Italy. The authors
are very grateful to Luigi Ambrosio and Francesco Serra Cassano for making their preprints available to them, for listening
with patience and for many unvaluable suggestions. 相似文献
6.
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
7.
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
8.
Fardoun Ali Regbaoui Rachid 《Calculus of Variations and Partial Differential Equations》2003,17(1):1-16
We study developing singularities for surfaces of rotation with free boundaries and evolving under volume-preserving mean curvature flow. We show that singularities form a finite, discrete set along the axis of rotation. We prove a monotonicity formula and conclude that type I singularities are asymtotically cylindrical. 相似文献
9.
Gian Paolo Leonardi 《manuscripta mathematica》2002,107(1):111-133
We consider a certain variational problem on Caccioppoli partitions with countably many components, which models immiscible
fluids as well as variational image segmentation, and generalizes the well-known problem with prescribed mean curvature. We
prove existence and regularity results, and finally show some explicit examples of minimizers.
Received: 7 June 2001 / Revisied version: 8 October 2001 相似文献
10.
R. Aiyama K. Akutagawa 《Calculus of Variations and Partial Differential Equations》2002,14(4):399-428
The purpose of this paper is to study some uniqueness, existence and regularity properties of the Dirichlet problem at infinity
for proper harmonic maps from the hyperbolic m-space to the open unit n-ball with a specific incomplete metric. When m=n=2, harmonic solutions of this Dirichlet problem yield complete constant mean curvature surfaces in the hyperbolic 3-space.
Received: 25 January 2001 / Accepted: 23 February 2001 / Published online: 25 June 2001 相似文献
11.
Roger Moser 《manuscripta mathematica》2001,105(3):379-399
We prove existence and uniqueness of weakly harmonic maps from the unit ball in ℝ
n
(with n≥ 3) to a smooth compact target manifold within the class of maps with small scaled energy for suitable boundary data.
Received: 9 June 2000 / Revised version: 17 April 2001 相似文献
12.
Hölder continuity of harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature 总被引:1,自引:1,他引:0
Bent Fuglede 《Calculus of Variations and Partial Differential Equations》2003,16(4):375-403
This is an addendum to the recent Cambridge Tract “Harmonic maps between Riemannian polyhedra”, by J. Eells and the present
author. H?lder continuity of locally energy minimizing maps from an admissible Riemannian polyhedron X to a complete geodesic space Y is established here in two cases: (1) Y is simply connected and has curvature (in the sense of A.D. Alexandrov), or (2) Y is locally compact and has curvature , say, and is contained in a convex ball in Y satisfying bi-point uniqueness and of radius (best possible). With Y a Riemannian polyhedron, and in case (2), this was established in the book mentioned above, though with H?lder continuity taken in a weaker, pointwise
sense. For X a Riemannian manifold the stated results are due to N.J. Korevaar and R.M. Schoen, resp. T. Serbinowski.
Received: 10 October 2001 / Accepted: 20 November 2001 / Published online: 6 August 2002 相似文献
13.
Qun Chen 《Calculus of Variations and Partial Differential Equations》1999,8(2):91-107
In this paper, we consider the harmonic maps with potential from compact Riemannian manifold with boundary into a convex
ball in any Riemannian manifold. We will establish some general properties such as the maximum principles, uniqueness and
existence for these maps, and as an application of them, we derive existence and uniqueness result for the Dirichlet problem
of the Landau-Lifshitz equations.
Received: December 10, 1997 / Accepted: June 29, 1998 相似文献
14.
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
15.
Luigi Ambrosio Nicola Fusco John E. Hutchinson 《Calculus of Variations and Partial Differential Equations》2003,16(2):187-215
The paper is concerned with the higher regularity properties of the minimizers of the Mumford–Shah functional. It is shown
that, near to singular points where the scaled Dirichlet integral tends to 0, the discontinuity set is close to an Almgren
area minimizing set. As a byproduct, the set of singular points of this type has Hausdorff dimension at most N-2, N being the dimension of the ambient space. Assuming higher integrability of the gradient this leads to an optimal estimate
of the Hausdorff dimension of the full singular set.
Received: 5 July 2001 / Accepted: 29 November 2001 / Published online: 23 May 2002 相似文献
16.
Harmonic maps with potential 总被引:8,自引:0,他引:8
Ali Fardoun Andrea Ratto 《Calculus of Variations and Partial Differential Equations》1997,5(2):183-197
Let (M,g) and (N,h) be two Riemannian manifolds, and G:N →ℝ a given function. If f:M → N is a smooth map, we set E
G
(f)=12 ∫M [∣df∣2− 2G(f)]dv
g. We establish some variational properties and some existence results for the functional E
G
(f): in particular, we analyse the case of maps into a sphere.
Received April 29, 1996 / Accepted May 28, 1996 相似文献
17.
Giovanni Alberti Guy Bouchitté Gianni Dal Maso 《Calculus of Variations and Partial Differential Equations》2003,16(3):299-333
We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals
on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.
Received: 29 November 2001 / Published online: 29 April 2002 相似文献
18.
I. Fonseca G. Leoni R. Paroni 《Calculus of Variations and Partial Differential Equations》2003,17(3):283-309
It is proved that if , with p > 1, if is bounded in , , and if in then provided is 2-quasiconvex and satisfies some appropriate growth and continuity condition. Characterizations of the 2-quasiconvex envelope
when admissible test functions belong to BHp are provided.
Received: 10 October 2001 / Accepted: 8 May 2002 / Published online: 17 December 2002 相似文献
19.
Yi-Hu Yang 《manuscripta mathematica》2000,103(3):401-407
In this note, we will show that no nonuniform lattice of SO(n, 1)(n≥ 4) is the fundamental group of a quasi-compact K?hler manifold
Received: 18 July 2000 / Revised version: 4 September 2000 相似文献
20.
G. S. Weiss 《Calculus of Variations and Partial Differential Equations》2003,17(3):311-340
The equation where converges to the Dirac measure concentrated at with mass has been used as a model for the propagation of flames with high activation energy. For initial data that are bounded in
and have a uniformly bounded support, we study non-negative solutions of the Cauchy problem in as We show that each limit of is a solution of the free boundary problem in on (in the sense of domain variations and in a more precise sense). For a.e. time t the graph of u(t) has a unique tangent cone at -a.e. The free boundary is up to a set of vanishing measure the sum of a countably n-1-rectifiable set and of the set on which vanishes in the mean. The non-degenerate singular set is for a.e. time a countably n-1-rectifiable set. As key tools we introduce a monotonicity formula and, on the singular set, an estimate for the parabolic
mean frequency.
Received: 8 August 2001 / Accepted: 8 May 2002 / Published online: 5 September 2002
RID="a"
ID="a" Partially supported by a Grant-in-Aid for Scientific Research, Ministry of Education, Japan. 相似文献