A Canonical Formalism for Multiple Integral Problems in the Calculus of Variation. (Short Communication).
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Hanno Rund (1968)
Aequationes mathematicae
Michael Ortiz, Alexander Mielke (2008)
ESAIM: Control, Optimisation and Calculus of Variations
This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems and subsequently...
Alexander Mielke, Michael Ortiz (2007)
ESAIM: Control, Optimisation and Calculus of Variations
This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems and...
Ivan Hlaváček (1981)
Aplikace matematiky
Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.
Claus Gerhardt (1976)
Mathematische Zeitschrift
Heinrich Voss (2003)
Applications of Mathematics
In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.
Claus Gerhardt (1975)
Mathematische Zeitschrift
Avner Friedman, Robert Jensen (1975)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Voss, Heinrich (2003)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Lucas Döring, Radu Ignat, Felix Otto (2014)
Journal of the European Mathematical Society
We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called “domain walls” – in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors that differ by an angle . Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The...
E. Shargorodsky, J. F. Toland (2003)
Annales de l'I.H.P. Analyse non linéaire
Richard S. Falk (1976)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Andrew Lorent (2012)
ESAIM: Control, Optimisation and Calculus of Variations
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain Ω ⊂ ℝ2the functional is I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z whereubelongs to the subset of functions in W02,2(Ω) whose gradient (in the sense of trace) satisfiesDu(x)·ηx = 1 where ηx is the inward pointing unit normal to ∂Ω at x. In [Ann. Sc. Norm. Super. Pisa Cl....
Andrew Lorent (2012)
ESAIM: Control, Optimisation and Calculus of Variations
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain Ω ⊂ ℝ2 the functional is where u belongs to the subset of functions in whose gradient (in the sense of trace) satisfies Du(x)·ηx = 1 where ηx is the inward pointing unit normal ...
Fuchs, Martin, Seregin, Gregory (2000)
Journal of Convex Analysis
Luciano Battaia (1975)
Rendiconti del Seminario Matematico della Università di Padova
J. Hannon, M. Marcus, Victor J. Mizel (2003)
ESAIM: Control, Optimisation and Calculus of Variations
Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical mechanical...
J. Hannon, M. Marcus, Victor J. Mizel (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of orthodox crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical...
Lorenzo Fatibene, Mauro Francaviglia, S. Mercadante (2011)
Communications in Mathematics
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular...
Eric Bonnetier, Richard S. Falk, Michael A. Grinfeld (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute...
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