共查询到20条相似文献,搜索用时 15 毫秒
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Xueping Huang 《Journal of Mathematical Analysis and Applications》2012,393(2):377-388
We study the uniqueness class problem for a class of heat equations defined on weighted graphs. As an application, we recover the volume growth criterion for stochastic completeness of Grigor’yan, Huang and Masamune in the case of weighted graphs. 相似文献
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Andreas Gastel 《Mathematische Zeitschrift》2002,242(1):47-62
By constructing examples which are explicit up to solving an ODE, we prove that singularities of first kind exist for the
harmonic map and Yang-Mills heat flows. As a by-product, we also get a simplified proof of Ratto's/Ding's theorem about the
existence of harmonic Hopf constructions.
Received: 25 May 2000; in final form: 17 November 2000 / Published online: 25 June 2001 相似文献
4.
Jishan Fan Hongjun Gao Takayoshi Ogawa Futoshi Takahashi 《Mathematische Nachrichten》2012,285(16):1963-1968
We consider the regularity problem under the critical condition to the biharmonic map heat flow from ?4 to a smooth compact Riemannian manifold without boundary. Using Gagliardo‐Nirenberg inequalities and delicate estimates, the Serrin type regularity criterion for the smooth solutions of biharmonic map heat flow is obtained without assuming a smallness condition on the initial energy. Our result improved the results of Lamm in 5 and 6 and generalized the results of Chang, Wang, Yang 1 , Strzelecki 11 and Wang 13 , 14 to non‐stationary case. 相似文献
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Min-Chun Hong Changyou Wang 《Calculus of Variations and Partial Differential Equations》2005,23(4):425-450
For
and
, we show that any minimizing biharmonic map from
to Sk is smooth off a closed set whose Hausdorff dimension is at most n-5. When n = 5 and k = 4, for a parameter
we introduce a
-relaxed energy
of the Hessian energy for maps in
so that each minimizer
of
is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of
for
.Received: 5 April 2004, Accepted: 19 October 2004, Published online: 10 December 2004 相似文献
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Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma. 相似文献
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Huajun Gong Tobias Lamm Changyou Wang 《Calculus of Variations and Partial Differential Equations》2012,45(1-2):165-191
We consider the Dirichlet problem for biharmonic maps u from a bounded, smooth domain ${\Omega\subset\mathbb R^n (n\ge 5)}$ to a compact, smooth Riemannian manifold ${N\subset{\mathbb {R}}^l}$ without boundary. For any smooth boundary data, we show that if u is a stationary biharmonic map that satisfies a certain boundary monotonicity inequality, then there exists a closed subset ${\Sigma\subset\overline{\Omega}}$ , with ${H^{n-4}(\Sigma)=0}$ , such that ${\displaystyle u\in C^\infty(\overline\Omega\setminus\Sigma, N)}$ . 相似文献
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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.
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Marcos T.O. Pimenta Sérgio H.M. Soares 《Journal of Mathematical Analysis and Applications》2012,390(1):274-289
Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti–Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. 相似文献
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In this paper, under an improved Hardy-Rellich's inequality, we study the existence of multiple and sign-changing solutions for a biharmonic equation in unbounded domain by the minimax method and linking theorem. 相似文献
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We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hölder continuous derivatives. This gives an extension of a result by Hildebrandt et al. (Acta Math 138:1–16, 1977) concerning harmonic maps. 相似文献
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This paper deals with the following class of singular biharmonic problems
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The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds. We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum of this operator exhibits some unexpected features: radial data may generate nonradial solutions. These boundary conditions are also of some interest in semilinear equations, since they enable us to give explicit radial singular solutions to fourth order Gelfand-type problems. 相似文献
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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
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Roger Moser 《Mathematische Zeitschrift》2003,243(2):263-289
Let be open and a smooth, compact Riemannian manifold without boundary. We consider the approximated harmonic map equation for maps , where . For , we prove H?lder continuity for weak solution s which satisfy a certain smallness condition. For , we derive an energy estimate which allows to prove partial regularity for stationary solutions of the heat flow for harmonic
maps in dimension .
Received: 7 May 2001; / in final form: 22 February 2002 Published online: 2 December 2002 相似文献
20.
Professor Haruo Totoki 《Probability Theory and Related Fields》1970,15(2):157-167
Summary A special flow, in which the basic automorphism is a Bernoulli automorphism and the ceiling function depends only on the present position of the Bernoulli sequence and is not lattice distributed, is a K-flow.This paper represents the result, in a revised form, which was presented at the Symposium on Ergodic Theory held at Mathematisches Forschungsinstitut Oberwolfach from August 4 to 10, 1968. 相似文献