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Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian

D. Le Peutrec (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

This article follows the previous works [HeKlNi, HeNi] by Helffer-Klein-Nier and Helffer-Nier about the metastability in reversible diffusion processes via a Witten complex approach. Again, exponentially small eigenvalues of some self-adjoint realization of Δ f , h ( 0 ) = - h 2 Δ + ∇ f ( x ) 2 - h Δ f ( x ) are considered as the small parameter h > 0 tends to 0 . The function f is assumed to be a Morse function on some bounded domain Ω with boundary ∂ Ω . Neumann type boundary conditions are considered. With these boundary conditions, some possible simplifications...

Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method

Jindřich Nečas, Ivan Hlaváček (1983)

Aplikace matematiky

A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.

Solution of the inverse problem of the calculus of variations

Jan Chrastina (1994)

Mathematica Bohemica

Given a family of curves constituting the general solution of a system of ordinary differential equations, the natural question occurs whether the family is identical with the totality of all extremals of an appropriate variational problem. Assuming the regularity of the latter problem, effective approaches are available but they fail in the non-regular case. However, a rather unusual variant of the calculus of variations based on infinitely prolonged differential equations and systematic use of...

Some concepts of regularity for parametric multiple-integral problems in the calculus of variations

M. Crampin, D. J. Saunders (2009)

Czechoslovak Mathematical Journal

We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter ( m + 1 ) -form are holonomic.

Some constructions of biharmonic maps on the warped product manifolds

Abdelmadjid Bennouar, Seddik Ouakkas (2017)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we characterize a class of biharmonic maps from and between product manifolds in terms of the warping function. Examples are constructed when one of the factors is either Euclidean space or sphere.

Some critical almost Kähler structures

Takashi Oguro, Kouei Sekigawa (2008)

Colloquium Mathematicae

We consider the set of all almost Kähler structures (g,J) on a 2n-dimensional compact orientable manifold M and study a critical point of the functional ℱ λ , μ ( J , g ) = ∫ M ( λ τ + μ τ * ) d M g with respect to the scalar curvature τ and the *-scalar curvature τ*. We show that an almost Kähler structure (J,g) is a critical point of ℱ - 1 , 1 if and only if (J,g) is a Kähler structure on M.

Some examples of harmonic maps for g -natural metrics

Mohamed Tahar Kadaoui Abbassi, Giovanni Calvaruso, Domenico Perrone (2009)

Annales mathématiques Blaise Pascal

We produce new examples of harmonic maps, having as source manifold a space ( M , g ) of constant curvature and as target manifold its tangent bundle T M , equipped with a suitable Riemannian g -natural metric. In particular, we determine a family of Riemannian g -natural metrics G on T 𝕊 2 , with respect to which all conformal gradient vector fields define harmonic maps from 𝕊 2 into ( T 𝕊 2 , G ) .

Some geometric aspects of the calculus of variations in several independent variables

David Saunders (2010)

Communications in Mathematics

This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.

Some perturbation results for non-linear problems

Carlo Carminati (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.

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