Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Filip Rindler"'
Autor:
Guido De Philippis, Filip Rindler
Publikováno v:
Mathematics in Engineering, Vol 2, Iss 3, Pp 386-422 (2020)
In this survey we collect some recent results obtained by the authors and collaborators concerning the fine structure of functions of bounded deformation (BD). These maps are L1-functions with the property that the symmetric part of their distributio
Externí odkaz:
https://doaj.org/article/fb275e651cc14b6cb6c95706df5b5f93
Publikováno v:
Archive for Rational Mechanics and Analysis. 239:1667-1731
We consider evolutionary PDE inclusions of the form $$\begin{aligned} -\lambda {\dot{u}}_\lambda + \Delta u - \mathrm {D}W_0(u) + f \ni \partial \mathscr {R}_1({\dot{u}}) \quad \text {in}\,\,{ (0,T) \times \Omega ,} \end{aligned}$$ where $$\mathscr {
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a81b9ce1ef9a966e9ff5917cba163936
https://doi.org/10.1007/s00205-020-01599-z
https://doi.org/10.1007/s00205-020-01599-z
Autor:
Filip Rindler, Guido De Philippis
Publikováno v:
Mathematics in Engineering, Vol 2, Iss 3, Pp 386-422 (2020)
In this survey we collect some recent results obtained by the authors and collaborators concerning the fine structure of functions of bounded deformation (BD). These maps are $\mathrm{L}^1$-functions with the property that the symmetric part of their
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98cf47eb1c50288ede5bc11e2d203ed2
https://www.aimspress.com/article/10.3934/mine.2020018/fulltext.html
https://www.aimspress.com/article/10.3934/mine.2020018/fulltext.html
Publikováno v:
Communications on Pure and Applied Mathematics
Communications on Pure and Applied Mathematics, Wiley, 2021, 74 (9), pp.1801-2022
Communications on Pure and Applied Mathematics, Wiley, 2021, 74 (9), pp.1801-2022
This work is concerned with an asymptotic analysis, in the sense of $\Gamma$-convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity. The study is performed as the damaged zone concentrates into a se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43898f8a71f6925cde029f69df2a38b5
http://wrap.warwick.ac.uk/131666/7/WRAP-concentration-versus-oscillation-effects-brittle-damage-Rindler-2019.pdf
http://wrap.warwick.ac.uk/131666/7/WRAP-concentration-versus-oscillation-effects-brittle-damage-Rindler-2019.pdf
Publikováno v:
Geometric and Functional Analysis
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In particular, o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f416ca521289bf51ac3db08df4660ea3
https://doi.org/10.1007/s00039-019-00497-1
https://doi.org/10.1007/s00039-019-00497-1
Autor:
Giles Shaw, Filip Rindler
Publikováno v:
Archive for Rational Mechanics and Analysis
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 $(u_j)_j \in \mathrm{BV}(\Omega;\mathbb{R}^m)$ under weak* convergence. These tools are then used
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3fe05ad87ca8ef22bdffc8f5e1a2c185
http://wrap.warwick.ac.uk/112433/13/WRAP-Liftings-Young-Measure-Shaw-2018.pdf
http://wrap.warwick.ac.uk/112433/13/WRAP-Liftings-Young-Measure-Shaw-2018.pdf
Autor:
Filip Rindler, David K. E. Green
Publikováno v:
UNCECOMP 2019 3rd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering
Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019)
Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019)
Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore not well s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be46175975c90f3f1713090a067e575b
Publikováno v:
The Quarterly Journal of Mathematics. 67:439-466
We prove a characterization result in the spirit of the Kinderlehrer-Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is the pointwise Jacobian is positive almost everyw
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f9d78069db0b002f06174265921e4d3
https://doi.org/10.1093/qmath/haw019
https://doi.org/10.1093/qmath/haw019
Autor:
Filip Rindler, Giles Shaw
Publikováno v:
SIAM Journal on Mathematical Analysis
We prove an integral representation theorem for the $\mathrm{L}^1(\Omega;\mathbb{R}^m)$-relaxation of the functional \[ \mathcal{F}\colon u\mapsto\int_\Omega f(x,u(x),\nabla u(x))\;\mathrm{dd } x,\quad u\in\mathrm{W}^{1,1}(\Omega;\mathbb{R}^m),\quad\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::37b822c39f1b14c9c41034637695a5a4
Autor:
Guido De Philippis, Filip Rindler
Publikováno v:
Proceedings of the International Congress of Mathematicians (ICM 2018)
The aim of this note is to present some recent results on the structure of the singular part of measures satisfying a PDE constraint and to describe some applications.
19 pages
19 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec3115bd21167d918c04adab4b1c1c00
http://hdl.handle.net/20.500.11767/118189
http://hdl.handle.net/20.500.11767/118189