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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 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 - 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.

Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Silvia Cingolani, Giuseppina Vannella (2001)

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

We present critical groups estimates for a functional f defined on the Banach space W 0 1 , p Ω , Ω bounded domain in R N , 2 < p < , associated to a quasilinear elliptic equation involving p -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of f in each critical point, we compute the critical groups of f in each isolated critical point via Morse index.

Currently displaying 21 – 40 of 85