31,649 research outputs found
Lipschitz stability estimate in the inverse Robin problem for the Stokes system
We are interested in the inverse problem of recovering a Robin coefficient
defined on some non accessible part of the boundary from available data on
another part of the boundary in the nonstationary Stokes system. We prove a
Lipschitz stability estimate under the \textit{a priori} assumption that the
Robin coefficient lives in some compact and convex subset of a finite
dimensional vectorial subspace of the set of continuous functions. To do so, we
use a theorem proved by L. Bourgeois which establishes Lipschitz stability
estimates for a class of inverse problems in an abstract framework
Bounding Stability Constants for Affinely Parameter-Dependent Operators
In this article we introduce new possibilities of bounding the stability
constants that play a vital role in the reduced basis method. By bounding
stability constants over a neighborhood we make it possible to guarantee
stability at more than a finite number of points and to do that in the offline
stage. We additionally show that Lyapunov stability of dynamical systems can be
handled in the same framework.Comment: Accepted version (C. R. Math.), 6 pages, 3 figure
A New Stability Result for Viscosity Solutions of Nonlinear Parabolic Equations with Weak Convergence in Time
We present a new stability result for viscosity solutions of fully nonlinear
parabolic equations which allows to pass to the limit when one has only weak
convergence in time of the nonlinearities
Stable pairs on elliptic K3 surfaces
We study semistable pairs on elliptic K3 surfaces with a section: we
construct a family of moduli spaces of pairs, related by wall crossing
phenomena, which can be studied to describe the birational correspondence
between moduli spaces of sheaves of rank 2 and Hilbert schemes on the surface.
In the 4-dimensional case, this can be used to get the isomorphism between the
moduli space and the Hilbert scheme described by Friedman.Comment: shortened version with French summary, to appear in C. R. Acad. Sci.
Paris. 6 page
A Note on Commuting Diffeomorphisms on Surfaces
Let S be a closed surface with nonzero Euler characteristic. We prove the
existence of an open neighborhood V of the identity map of S in the
C^1-topology with the following property: if G is an abelian subgroup of
Diff^1(S) generated by any family of elements in V then the elements of G have
common fixed points. This result generalizes a similar result due to Bonatti
and announced in his paper "Diffeomorphismes commutants des surfaces et
stabilite des fibrations en tores".Comment: 16 page
On the stability of flat complex vector bundles over parallelizable manifolds
We investigate the flat holomorphic vector bundles over compact complex
parallelizable manifolds , where is a complex connected Lie
group and is a cocompact lattice in it. The main result proved here is
a structure theorem for flat holomorphic vector bundles associated to
any irreducible representation . More precisely, we prove that is holomorphically isomorphic to
a vector bundle of the form , where is a stable vector
bundle. All the rational Chern classes of vanish, in particular, its degree
is zero.
We deduce a stability result for flat holomorphic vector bundles
of rank 2 over . If an irreducible representation satisfies the conditionmthat the
induced homomorphism does not
extend to a homomorphism from , then is proved to be stable.Comment: Comptes Rendus Math\'ematique (to appear
About the stability of the tangent bundle restricted to a curve
Let C be a smooth projective curve with genus g>1 and Clifford index c(C) and
let L be a line bundle on C generated by its global sections. The morphism i:C
-->P(H^0(L))=P is well-defined and i*T is the restriction to C of the tangent
bundle T of the projective space P. Sharpening a theorem by Paranjape, we show
that if deg L>2g-c(C)-1 then i*T is semi-stable, specifying when it is also
stable. We then prove the existence on many curves of a line bundle L of degree
2g-c(C)-1 such that i*T is not semi-stable. Finally, we completely characterize
the (semi-)stability of i*T when C is hyperelliptic.Comment: 5 page
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