- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 07:26:13
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JEMS&vol=16&iss=3&update_since=2024-03-29
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
16
2014
3
On periodic homogenization in perfect elasto-plasticity
Gilles
Francfort
Université Paris-Nord, VILLETANEUSE, FRANCE
Alessandro
Giacomini
Università degli Studi di Brescia, BRESCIA, ITALY
Elasticity, plasticity, space of bounded deformations, lower semicontinuity, Radon measures, periodic homogenization, evolution problems
The limit behavior of a periodic assembly of a finite number of elasto-plastic phases is investigated as the period becomes vanishingly small. A limit quasi-static evolution is derived through two-scale convergence techniques. It can be thermodynamically viewed as an elasto-plastic model, albeit with an infinite number of internal variables.
Mechanics of deformable solids
Partial differential equations
Operator theory
Calculus of variations and optimal control; optimization
409
461
10.4171/JEMS/437
http://www.ems-ph.org/doi/10.4171/JEMS/437
Generalized holomorphic analytic torsion
José Ignacio
Burgos Gil
, MADRID, SPAIN
Gerard
Freixas i Montplet
C.N.R.S. - Institut de Mathématiques de Jussieu, PARIS CEDEX 05, FRANCE
Răzvan
Liţcanu
University “Al. I. Cuza”, IAȘI, ROMANIA
Grothendieck–Riemann–Roch theorem, holomorphic analytic torsion, Quillen metric, Grothendieck duality
In this paper we extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for projective morphisms. The extension of the holomorphic analytic torsion classes of Bismut and K¨ohler is obtained as the theory of generalized analytic torsion classes associated to $–R=2$, $R$ being the $R$-genus. As an application of the axiomatic characterization, we give new simpler proofs of known properties of holomorpic analytic torsion classes, we give a characterization of the $R$-genus, and we construct a direct image of hermitian structures for projective morphisms.
Algebraic geometry
General
Several complex variables and analytic spaces
463
535
10.4171/JEMS/438
http://www.ems-ph.org/doi/10.4171/JEMS/438
Finiteness problems on Nash manifolds and Nash sets
José
Fernando
Universidad Complutense de Madrid, MADRID, SPAIN
José Manuel
Gamboa
Universidad Complutense de Madrid, MADRID, SPAIN
Jesús
Ruiz
Universidad Complutense de Madrid, MADRID, SPAIN
Finiteness, Nash functions and Nash sets, semialgebraic sets, Nash manifolds with corners, extension, normal crossings at a point, normal crossings divisor
We study here several finiteness problems concerning affine Nash manifolds $M$ and Nash subsets $X$. Three main results are: (i) A Nash function on a semialgebraic subset $Z$ of $M$ has a Nash extension to an open semialgebraic neighborhood of $Z$ in $M$, (ii) A Nash set $X$ that has only normal crossings in $M$ can be covered by finitely many open semialgebraic sets $U$ equipped with Nash diffeomorphisms $(u_1,\dots,u_m):U\to\mathbb R^m$ such that $U\cap X=\{u_1\cdots u_r=0\}$, (iii) Every affine Nash manifold with corners $N$ is a closed subset of an affine Nash manifold $M$ where the Nash closure of the boundary $\partial N$ of $N$ has only normal crossings and $N$ can be covered with finitely many open semialgebraic sets $U$ such that each intersection $N\cap U=\{u_1\ge0,\dots u_r\ge0\}$ for a Nash diffeomorphism $(u_1,\dots,u_m):U\to\mathbb R^m$.
Algebraic geometry
General
Several complex variables and analytic spaces
Global analysis, analysis on manifolds
537
570
10.4171/JEMS/439
http://www.ems-ph.org/doi/10.4171/JEMS/439
Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems
Andrea
Cianchi
Universita di Firenze, FIRENZE, ITALY
Vladimir
Maz'ya
Linköping University, LINKÖPING, SWEDEN
Nonlinear elliptic equations, Dirichlet problems, Neumann problems, gradient estimates, rearrangements, Lorentz spaces, Orlicz spaces
A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.
Partial differential equations
General
571
595
10.4171/JEMS/440
http://www.ems-ph.org/doi/10.4171/JEMS/440
On normal subgroups of compact groups
Nikolay
Nikolov
University of Oxford, OXFORD, UNITED KINGDOM
Dan
Segal
University of Oxford, OXFORD, UNITED KINGDOM
Compact groups, dense normal subgroups, closed normal subgroups, conjugacy width
Among compact Hausdorff groups $G$ whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup $[H, G]$ is closed for every closed normal subgroup $H$ of $G$.
Topological groups, Lie groups
General
Group theory and generalizations
597
618
10.4171/JEMS/441
http://www.ems-ph.org/doi/10.4171/JEMS/441