O 19. a 20. Hilbertově problému
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Displaying 1 – 20 of 119
Of the structure of the Euler mapping
Demeter Krupka (1974)
Archivum Mathematicum
On a class of variational integrals over BV varieties
Primo Brandi, Anna Salvadori (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.
On a class of variational problems defined by polynomial Lagrangians
Demeter Krupka (1976)
Archivum Mathematicum
On a conjecture by Auerbach
Nicola Fusco, A. Pratelli (2011)
Journal of the European Mathematical Society
In 1938 Herman Auerbach published a paper where he showed a deep connection between the solutions of the Ulam problem of floating bodies and a class of sets studied by Zindler, which are the planar sets whose bisecting chords all have the same length. In the same paper he conjectured that among Zindler sets the one with minimal area, as well as with maximal perimeter, is the so-called “Auerbach triangle”. We prove this conjecture.
On a critical point theory for minimal surfaces spanning a wire in Rn.
Michael Struwe (1984)
Journal für die reine und angewandte Mathematik
On a functional depending on curvature and edges
Carlo-Romano Grisanti (2001)
Rendiconti del Seminario Matematico della Università di Padova
On a general coarea inequality and applications.
Magnani, Valentino (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
On a magnetic characterization of spectral minimal partitions
Bernard Helffer, Thomas Hoffmann-Ostenhof (2013)
Journal of the European Mathematical Society
Given a bounded open set in (or in a Riemannian manifold) and a partition of by open sets , we consider the quantity where is the ground state energy of the Dirichlet realization of the Laplacian in . If we denote by the infimum over all the -partitions of , a minimal -partition is then a partition which realizes the infimum. When , we find the two nodal domains of a second eigenfunction, but the analysis of higher ’s is non trivial and quite interesting. In this paper, we give...
On a problem of Monge.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
On a system of partial differential equations in Heisenberg space. (Sur un système d'équations aux d'érivées partielles dans l'espace de Heisenberg.)
Bekkar, M. (2001)
Rendiconti del Seminario Matematico
On a Theorem of de Giorgi and Stampacchia.
Leon Simon (1977)
Mathematische Zeitschrift
On a variant of Korn’s inequality arising in statistical mechanics
L. Desvillettes, Cédric Villani (2002)
ESAIM: Control, Optimisation and Calculus of Variations
We state and prove a Korn-like inequality for a vector field in a bounded open set of , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case are...
On a variant of Korn's inequality arising in statistical mechanics
L. Desvillettes, Cédric Villani (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We state and prove a Korn-like inequality for a vector field in a bounded open set of , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case...
On a variational property of integral functionals and related conjectures
Biagio Ricceri (1996)
Banach Center Publications
The aim of this paper is to give the proofs of those results that in [4] were only announced, and, at the same time, to propose some possible developments, indicating some of the most significant open problems.
On a variational theory of image amodal completion
Simon Masnou, Jean-Michel Morel (2006)
Rendiconti del Seminario Matematico della Università di Padova
On an optimal shape design problem in conduction
José Carlos Bellido (2006)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.
On calibrations for Lawson’s cones
Andrea Davini (2004)
Rendiconti del Seminario Matematico della Università di Padova
On computer aided shape optimization
Raino Mäkinen (1993)
Kybernetika
On Conditions for Unrectifiability of a Metric Space
Piotr Hajłasz, Soheil Malekzadeh (2015)
Analysis and Geometry in Metric Spaces
We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.
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