共查询到20条相似文献，搜索用时 31 毫秒
1.
Generalised twists,stationary loops,and the Dirichlet energy over a space of measure preserving maps
M. S. Shahrokhi-Dehkordi A. Taheri 《Calculus of Variations and Partial Differential Equations》2009,35(2):191-213
Let be a bounded Lipschitz domain and consider the Dirichlet energy functional
over the space of measure preserving maps
In this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler–Lagrange equations associated with over . The main result here is that in even dimensions the latter equations admit infinitely many solutions, modulo isometries, amongst such maps. We investigate various qualitative properties of these solutions in view of a remarkably interesting
previously unknown explicit formula. 相似文献
2.
Alessandro Perotti 《Advances in Applied Clifford Algebras》2009,19(2):441-451
We study Fueter-biregular functions of one quaternionic variable. We consider left-regular functions in the kernel of the
Cauchy–Riemann operator
. A quaternionic function is biregular if on Ω, f is invertible and . Every continuous map p from Ω to the sphere of unit imaginary quaternions induces an almost complex structure Jp on the tangent bundle of . Let be the space of (pseudo)holomorphic maps from (Ω, Jp) to (), where Lp is the almost complex structure defined by left multiplication by p. Every element of is regular, but there exist regular functions that are not holomorphic for any p. The space of biregular functions contains the invertible elements of the spaces . By means of a criterion, based on the energy-minimizing property of holomorphic maps, that characterizes holomorphic functions
among regular functions, we show that every biregular function belongs to some space .
Received: October, 2007. Accepted: February, 2008. 相似文献
3.
Zhaoli Liu Jiabao Su Zhi-Qiang Wang 《Calculus of Variations and Partial Differential Equations》2009,35(4):463-480
In this paper, we study existence of nontrivial solutions to the elliptic equation
and to the elliptic system
where Ω is a bounded domain in with smooth boundary ∂Ω, , f (x, 0) = 0, with m ≥ 2 and . Nontrivial solutions are obtained in the case in which the nonlinearities have linear growth. That is, for some c > 0, for and , and for and , where I
m
is the m × m identity matrix. In sharp contrast to the existing results in the literature, we do not make any assumptions at infinity
on the asymptotic behaviors of the nonlinearity f and .
Z. Liu was supported by NSFC(10825106, 10831005). J. Su was supported by NSFC(10831005), NSFB(1082004), BJJW-Project(KZ200810028013)
and the Doctoral Programme Foundation of NEM of China (20070028004). 相似文献
4.
Simon Raulot 《Mathematische Zeitschrift》2009,261(2):321-349
Let M be an n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric g, a spin structure σ and a chirality operator Γ. We define and study some properties of a spin conformal invariant given by:
where is the smallest eigenvalue of the Dirac operator under the chiral bag boundary condition . More precisely, we show that if n ≥ 2 then:
相似文献
5.
6.
J. V. Manojlović 《Lithuanian Mathematical Journal》2009,49(1):71-92
We consider a class of fourth-order nonlinear difference equations of the form
where α and β are the ratios of odd positive integers, and {p
n
} and {q
n
} are positive real sequences defined for all
satisfying the condition
We classify the nonoscillatory solutions of (Ω) and establish necessary and/or sufficient conditions for the existence of
nonoscillatory solutions with specific asymptotic behavior.
Supported by Ministry of Science, Technology and Development of Republic of Serbia – Grant No. 144003. 相似文献
7.
Futoshi Takahashi 《Archiv der Mathematik》2009,93(2):191-197
In this note, we consider the problem
on a smooth bounded domain Ω in for p > 1. Let u
p
be a positive solution of the above problem with Morse index less than or equal to . We prove that if u
p
further satisfies the assumption as p → ∞, then the number of maximum points of u
p
is less than or equal to m for p sufficiently large. If Ω is convex, we also show that a solution of Morse index one satisfying the above assumption has a
unique critical point and the level sets are star-shaped for p sufficiently large.
相似文献
8.
In the Heisenberg group framework, we obtain a geometric inequality for stable solutions of in a domain . More precisely, if we denote the horizontal intrinsic Hessian by Hu, the mean curvature of a level set by h, its imaginary curvature by p, the intrinsic normal by ν and the unit tangent by υ, we have that
for any . Stable solutions in the entire satisfying a suitably weighted energy growth and such that are then shown to have level sets with vanishing mean curvature.
F. Ferrari is partially supported by GALA project Geometric Analysis in Lie groups and Applications, supported by the European
Commission within the 6th Framework Programme and by the PRIN project Viscosity, metric and control theoretic methods in nonlinear
partial differential equations, MIUR (Italy). E. Valdinoci is partially supported by the PRIN project Variational Methods
and Nonlinear Differential Equations, MIUR (Italy). 相似文献
9.
The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations 总被引：1，自引：0，他引：1
Kentaro Hirata 《Mathematische Annalen》2008,340(3):625-645
We investigate the boundary growth of positive superharmonic functions u on a bounded domain Ω in , n ≥ 3, satisfying the nonlinear elliptic inequality
where c > 0, α ≥ 0 and p > 0 are constants, and is the distance from x to the boundary of Ω. The result is applied to show a Harnack inequality for such superharmonic functions. Also, we study
the existence of positive solutions, with singularity on the boundary, of the nonlinear elliptic equation
where V and f are Borel measurable functions conditioned by the generalized Kato class. 相似文献
10.
A maximal surface with isolated singularities in a complete flat Lorentzian 3-manifold
is said to be entire if it lifts to a (periodic) entire multigraph in . In addition, is called of finite type if it has finite topology, finitely many singular points and is a finitely sheeted multigraph. Complete (or proper) maximal immersions with isolated singularities in are entire, and entire embedded maximal surfaces in with a finite number of singularities are of finite type. We classify complete flat Lorentzian 3-manifolds carrying entire
maximal surfaces of finite type, and deal with the topology, Weierstrass representation and asymptotic behavior of this kind
of surfaces. Finally, we construct new examples of periodic entire embedded maximal surfaces in with fundamental piece having finitely many singularities.
相似文献
11.
12.
Annalisa Malusa Luigi Orsina 《Calculus of Variations and Partial Differential Equations》2006,27(2):179-202
We study the limit as n goes to +∞ of the renormalized solutions u
n
to the nonlinear elliptic problems
where Ω is a bounded open set of ℝ
N
, N≥ 2, and μ is a Radon measure with bounded variation in Ω. Under the assumption of G-convergence of the operators , defined for , to the operator , we shall prove that the sequence (u
n
) admits a subsequence converging almost everywhere in Ω to a function u which is a renormalized solution to the problem
相似文献
13.
Nicola Garofalo 《manuscripta mathematica》2008,126(3):353-373
We prove some new a priori estimates for H
2-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H
2-convex function in vanishing on ∂Ω one has
.
Supported in part by NSF Grant DMS-07010001. 相似文献
14.
L. Chergui 《Journal of Evolution Equations》2009,9(2):405-418
For many evolution problems, a basic question is to establish convergence to equilibrium for globally defined solutions. This
type of result is well known for the semilinear wave equation with linear dissipation. In this paper, we are concerned with
the asymptotic behavior of global and bounded solutions of the following semilinear wave equation
with homogeneous Dirichlet boundary conditions and initial conditions. Here, α ≥ 0, is a bounded domain with sufficiently smooth boundary and is analytic in the second variable, uniformly with respect to the first one. In this paper, we suppose that the set of stationary
solutions is compact and we prove convergence of global and bounded solutions to an equilibrium, for some small value of α depending on the nonlinearity f. The case α = 0 corresponds to the wave equation with linear dissipation which is solved by Haraux and Jendoubi (Calc Var Partial Differ
Equ 9:95–124, 1999). 相似文献
15.
16.
An analog of the classical Fourier formula for the characteristic function of a convex compact set
is considered:
where W is a polyhedral in
. Bibliography: 6 titles. 相似文献
17.
Quasiminima of the Lipschitz extension problem 总被引：1，自引：0，他引：1
Petri Juutinen 《Annali di Matematica Pura ed Applicata》2007,186(2):303-316
In this paper, we extend the notion of quasiminimum to the framework of supremum functionals by studying the model case
which governs the real analysis problem of finding optimal Lipschitz extensions. Using a characterization involving the concept
of comparison with cones, we obtain a Harnack inequality, Lipschitz estimates and various convergence and stability properties
for the quasiminima. Several examples of quasiminima are also given.
Mathematics Subject Classification (2000) 47J20, 49N60, 35B65 相似文献
18.
Robert Černý 《Calculus of Variations and Partial Differential Equations》2007,28(2):203-216
We compute the relaxation
where
for sequences of functions from
converging strongly in the
-norm to
. 相似文献
19.
Hoai-Minh Nguyen 《Journal d'Analyse Mathématique》2007,101(1):367-395
In this paper, we prove the estimate
, for every δ ∈ (0, ℓN), where C = C(N) is a positive constant depending only on N and
. We show that the constant ℓN in this estimate is optimal. We also present a class of maps from
into
, strictly larger than
, on which we can define the notion of degree and for which the previous inequality still holds. 相似文献
20.
M. Foss 《Annali di Matematica Pura ed Applicata》2008,187(2):263-321
We prove some global, up to the boundary of a domain $\Omega \subset {\mathbb{R}}^{n}We prove some global, up to the boundary of a domain , continuity and Lipschitz regularity results for almost minimizers of functionals of the form
The main assumption for g is that it be asymptotically convex with respect its third argument. For the continuity results, the integrand is allowed
to have some discontinuous behavior with respect to its first and second arguments. For the global Lipschitz regularity result,
we require g to be H?lder continuous with respect to its first two arguments.
相似文献