Results 1 to 10 of about 336 (182)
Entropy, 2021 We construct a 2-categorical extension of the relative entropy functor of Baez and Fritz, and show that our construction is functorial with respect to vertical morphisms.
James Fullwood
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Compactness and lower semicontinuity in $GSBD$ [PDF]
Journal of the European Mathematical Society, 2020 In this paper we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in ( G )
Chambolle, Antonin, Crismale, Vito
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On the Lower Semicontinuity of Supremal Functionals [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2003 Summary: In this paper we study the lower semicontinuity problem for a supremal functional of the form \[ F(u,\Omega )= \underset {x\in \Omega } {\text{ess\,sup}} f(x,u(x),Du(x)) \] with respect to the strong convergence in \(L^\infty (\Omega )\), furnishing a comparison with the analogous theory developed by Serrin for integrals.
GORI, MICHELE, MAGGI, FRANCESCO
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A categorical characterization of relative entropy on standard Borel spaces [PDF]
Logical Methods in Computer Science, 2023 We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces.
Nicolas Gagne, Prakash Panangaden
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Some Variational Results Using Generalizations of Sequential Lower Semicontinuity
Fixed Point Theory and Applications, 2010 Kirk and Saliga and then Chen et al. introduced lower semicontinuity from above, a generalization of sequential lower semicontinuity, and they showed that well-known results, such as Ekeland's variational principle and Caristi's fixed point theorem ...
Bottaro Aruffo Ada, Bottaro Gianfranco
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Some remarks on Lower semicontinuity [PDF]
Indiana University Mathematics Journal, 2000 The paper is aimed to the extension of some classical lower semicontinuity results of J. Serrin concerning lower semicontinuity of integral functionals \[ u\mapsto \int_\Omega L\bigl(x,u(x),\nabla u(x)\bigr) dx \] for real-valued functions \(u\). Serrin considered two kinds of convergence, according to the growth condition of the Lagrangian: \(L^1 ...
Fonseca, Irene, Leoni, Giovanni
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The stability of minimal solution sets for set optimization problems via improvement sets
Journal of Inequalities and Applications, 2023 In this paper we investigate the stability of solution sets for set optimization problems via improvement sets. Some sufficient conditions for the upper semicontinuity, lower semicontinuity, and compactness of E-minimal solution mappings are given for ...
Taiyong Li, Yanhui Wei
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Lower semicontinuity for the Helfrich problem [PDF]
Annals of Global Analysis and Geometry, 2020 AbstractWe minimise the Canham–Helfrich energy in the class of closed immersions with prescribed genus, surface area, and enclosed volume. Compactness is achieved in the class of oriented varifolds. The main result is a lower-semicontinuity estimate for the minimising sequence, which is in general false under varifold convergence by a counter example ...
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Liftings, Young Measures, and Lower Semicontinuity [PDF]
Archive for Rational Mechanics and Analysis, 2018 This work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs $(u_j,Du_j)j$ for $(u_j)_j \in \mathrm{BV}(Ω;\mathbb{R}^m)$ under weak* convergence. These tools are then used to prove an integral representation theorem for the relaxation of the functional \[ \mathcal{F}\colon u\to ...
Filip Rindler, Giles Shaw
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Semicontinuity and closedness of parametric generalized lexicographic quasiequilibrium problems
Journal of Inequalities and Applications, 2016 This paper is mainly concerned with the upper semicontinuity, closedness, and the lower semicontinuity of the set-valued solution mapping for a parametric lexicographic equilibrium problem where both two constraint maps and the objective bifunction ...
Rabian Wangkeeree +2 more
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