共查询到20条相似文献,搜索用时 62 毫秒
1.
We prove a regularity result for critical points of the polyharmonic energy in with and p > 1. Our proof is based on a Gagliardo–Nirenberg-type estimate and avoids the moving frame technique. In view of the monotonicity
formulae for stationary harmonic and biharmonic maps, we infer partial regularity in theses cases. 相似文献
2.
Z. Abdulhadi 《Journal of Mathematical Analysis and Applications》2008,338(1):705-709
In this paper, we show the existence of Landau constant for biharmonic mappings of the form F(z)=2|z|G(z)+K(z), |z|<1, where G and K are harmonic. 相似文献
3.
Ye-Lin Ou 《Annals of Global Analysis and Geometry》2009,36(2):133-142
This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension
field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface
into Euclidean 3-space. As applications, we construct a two-parameter family of non-minimal conformal biharmonic immersions
of cylinder into and some examples of conformal biharmonic immersions of four-dimensional Euclidean space into sphere and hyperbolic space,
thus providing many simple examples of proper biharmonic maps with rich geometric meanings. These suggest that there are abundant
proper biharmonic maps in the family of conformal immersions. We also explore the relationship between biharmonicity and holomorphicity
of conformal immersions of surfaces.
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4.
We show that a conformal mapping between Riemannian manifolds of the same dimension n ≥ 3 is biharmonic if and only if the gradient of its dilation satisfies a certain second-order elliptic partial differential
equation. On an Einstein manifold solutions can be generated from isoparametric functions. We characterise those semi-conformal
submersions that are biharmonic in terms of their dilation and the fibre mean curvature vector field.
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5.
Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere. 相似文献
6.
Michael Ulm 《Proceedings of the American Mathematical Society》1999,127(2):481-489
For an operator on a Banach lattice we examine the interval on the real line for which the resolvent is positive. This positivity interval is then explicitly calculated for the biharmonic operator with three different boundary conditions.
7.
Rodrigo P. Gomez 《Transactions of the American Mathematical Society》2001,353(5):1741-1753
In this article we demonstrate that every harmonic map from a closed Riemannian manifold into a Hilbert Grassmannian has image contained within a finite-dimensional Grassmannian.
8.
Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalize harmonic maps. We consider the Hopf map and modify it into a nonharmonic biharmonic map . We show to be unstable and estimate its biharmonic index and nullity. Resolving the spectrum of the vertical Laplacian associated to the Hopf map, we recover Urakawa's determination of its harmonic index and nullity.
9.
C. Greco 《Proceedings of the American Mathematical Society》2001,129(4):1199-1206
We consider the problem of minimizing the energy of the maps from the annulus to such that is equal to for , and to , for , where is a fixed angle.
We prove that the minimum is attained at a unique harmonic map which is a planar map if , while it is not planar in the case \pi^2$">.
Moreover, we show that tends to as , where minimizes the energy of the maps from to , with the boundary condition , .
10.
We show that harmonic maps from 2-dimensional Euclidean polyhedra to arbitrary NPC spaces are totally geodesic or constant
depending on a geometric and combinatorial condition of the links of the 0-dimensional skeleton. Our method is based on a
monotonicity formula rather than a codimension estimate of the singular set as developed by Gromov–Schoen or the mollification
technique of Korevaar–Schoen.
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11.
Rachel J. Weir 《Journal of Mathematical Analysis and Applications》2003,288(2):383-396
A constructive proof is given of the existence of the weighted biharmonic Green function Γα for α?0. The method is used to derive the explicit formula for Γ1 previously stated by Hedenmalm. In addition, a formula for Γ2 is found, which is then shown to take both positive and negative values in the bidisk . 相似文献
12.
Contrary to the second-order case, biharmonic heat kernels are sign-changing. A deep knowledge of their behaviour may however allow us to prove positivity results for solutions of the Cauchy problem. We establish further properties of these kernels, we prove some Lorch–Szegö-type monotonicity results and we give some hints on how to obtain similar results for higher order polyharmonic parabolic problems. 相似文献
13.
Tatiana V. Savina 《Journal of Mathematical Analysis and Applications》2010,370(2):716-1163
The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflection formulas for the biharmonic functions u(x,y)∈R2 subject to different boundary conditions on a real-analytic curve in the plane. The obtained formulas, generalizing the celebrated Schwarz symmetry principle for harmonic functions, have different structures. In particular, in the special case of the boundary, Γ0:={y=0}, reflections are point-to-point when the given on Γ0 conditions are u=n∂u=0, u=Δu=0 or n∂u=n∂Δu=0, and point to a continuous set when u=n∂Δu=0 or n∂u=Δu=0 on Γ0. 相似文献
14.
In this paper, we study the blow up of a sequence of (both extrinsic and intrinsic) biharmonic maps in dimension four with bounded energy and show that there is no neck in this process. Moreover, we apply the method to provide new proofs to the removable singularity theorem and energy identity theorem of biharmonic maps. 相似文献
15.
This paper is devoted to the introduction of a mixed finite element for the solution of the biharmonic problem. We prove optimal rate of convergence for the element. The mixed approach allows the simultaneous approximation of both displacement and tensor of its second derivatives. 相似文献
16.
We consider closed biharmonic hypersurfaces in a Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms. As an application of this formula, we reobtain a result concerning the closed biharmonic hypersurfaces in Euclidean spheres that lie in a closed hemisphere. 相似文献
17.
This article discusses the hypothesis that the universally conserved stress-energy tensor of matter is the source of the gravitational
field. From this hypothesis, it immediately follows that space-time must be Riemannian. In contrast to the general theory
of relativity, in the gravitational theory based on this hypothesis, the concept of an inertial coordinate system, acceleration
relative to space, and the laws of conservation of the energy and angular momenta are retained. In the framework of this theory,
the gravitational field is a physical field. The theory explains all observable facts of the solar system, predicts the existence
of a large hidden mass of matter in a homogeneous and isotropic universe, and assumes that such a universe can only be “flat.”
The theory changes the established idea of the collapse of large massive bodies.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 5–24, January, 1997. 相似文献
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20.
Ibtesam O. Bajunaid David Singman 《Journal of Mathematical Analysis and Applications》2011,378(2):710-722
Let T be a tree rooted at e endowed with a nearest-neighbor transition probability that yields a recurrent random walk. We show that there exists a function K biharmonic off e whose Laplacian has potential theoretic importance and, in addition, has the following property: Any function f on T which is biharmonic outside a finite set has a representation, unique up to addition of a harmonic function, of the form f=βK+B+L, where β a constant, B is a biharmonic function on T, and L is a function, subject to certain normalization conditions, whose Laplacian is constant on all sectors sufficiently far from the root. We obtain a characterization of the functions biharmonic outside a finite set whose Laplacian has 0 flux similar to one that holds for a function biharmonic outside a compact set in Rn for n=2,3, and 4 proved by Bajunaid and Anandam. Moreover, we extend the definition of flux and, under certain restrictions on the tree, we characterize the functions biharmonic outside a finite set that have finite flux in this extended sense. 相似文献