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1.
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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2.
3.
Wengui Yang Ahmed Alsaedi Tasawar Hayat Habib M. Fardoun 《Mathematical Methods in the Applied Sciences》2019,42(14):4876-4888
This paper investigates the asymptotical stability of Riemann‐Liouville q‐fractional neutral systems with mixed delays (constant time delay and distributed delay). By constructing some appropriate Lyapunov‐Kravsovskii functionals, some sufficient conditions on delay‐dependent and delay‐independent asymptotical stability are obtained in terms of linear matrix inequality (LMI). Our employed method is based on the direct calculation of quantum derivatives of the Lyapunov‐Kravsovskii functionals. Finally, two examples are presented to demonstrate the availability of our obtained results. 相似文献
4.
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
5.
On the Heat Flow for Harmonic Maps with Potential 总被引:2,自引:0,他引:2
Let (M, g) and (N, h) be twoconnected Riemannian manifolds without boundary (M compact,N complete). Let G C
(N): ifu: M N is a smooth map, we consider the functional E
G
(u) = (1/2)
M
[|du|2– 2G(u)]dV
M
and we study its associated heat equation. Inthe compact case, we recover a version of the Eells–Sampson theorem,while for noncompact target manifold N, we establishsuitable hypotheses and ensure global existence and convergence atinfinity. In the second part of the paper, we study phenomena of blowingup solutions. 相似文献
6.
Paul Baird Ali Fardoun Rachid Regbaoui 《Calculus of Variations and Partial Differential Equations》2006,27(1):75-104
We formulate an appropriate gradient flow in order to study the evolution of the Q-curvature to a prescribed function on a 4-manifold. For a class of prescribed functions, we show convergence and describe the asymptotic behaviour at infinity. 相似文献
7.
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
8.
[reaction: see text] Deprotection of oximes to their corresponding carbonyl compounds through the use of photosensitized electron-transfer reactions proceeds in reasonable to good yields. Better yields are obtained in nonpolar solvents and when triplet sensitizers are used. Preliminary mechanistic studies suggest the involvement of an iminoxyl radical. 相似文献
9.
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
10.
Ali Fardoun 《manuscripta mathematica》2005,116(1):57-69
We consider weakly p-harmonic maps (p2) from a compact connected Riemannian manifold Mm(m2) to the the standard sphere Sn with values in the closed hemisphere Sn+ = {x Sn : xn+1 0 } (n 2). We first prove that if u=(u1,...,un+1):MSn is a weakly p-harmonic map satisfying un+1(x)>0 a.e. on M, then it is a minimizing p-harmonic map. Next, we give a necessary and sufficient condition for the boundary data : M Sn+ to achieve uniqueness; and when this condition fails, we are able to describe the set of all minimizers. When M is without boundary, we obtain a Liouville type Theorem for weakly p-harmonic maps.Mathematics Subject Classification (2000): 58E20; 35J70 相似文献