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Robust control via sequential semidefinite programming. (English summary

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Computing local integral closures. (English summary

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Milnor fibration and fibred links at infinity

Reviewed by H. Vishnu Hebbar References

Quadratic variations along irregular subdivisions for Gaussian processes. (English summary) Electron. J. Probab. 10 (2005), no. 20, 691–717 (electronic). The author extends the theory on singularity functions for fractional processes to a large class of subdivisions which may be irregular. It is proved that the limit of second-order quadratic variation depends on the structure of the subdivisions and the singularity function of the process. The results are illustrated with the example of the time-space deformed fractional Brownian motion

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Feedback boundary stabilization of the two-dimensional Navier-Stokes equations. (English summary) SIAM J. Control Optim. 45 (2006), no. 3, 790–828 (electronic). This paper examines the exponential stabilization of Navier-Stokes (NS) equations, around an unstable stationary solution, in a 2-dimensional bounded domain Ω. The goal is to study the local robustness of the feedback stabilization from the boundary of the NS solution, where the feedback law is a pointwise (in time) feedback law (one of the major differences with the works of Fursikov). This study is motivated by the fact that in real applications, pointwise feedback laws are more robust with respect to noises in models. Firstly the author studies the Oseen equations (linearized NS equations). He introduces the Oseen operator and formulates the boundary optimal control problem. Then finite and infinite time horizon control problems are studied and the optimality systems characterizing the optimal solutions are established. Secondly the stabilization of the NS equations, by using a linear feedback law is analyzed. Finally some additional results are presented, in particular the author compares his results with th

References

Homogenization of a one-dimensional spectral problem for a singularly perturbed elliptic operator with Neumann boundary conditions. (English summary) Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 1, 1–31.1553-524X This paper is devoted to the homogenization of a spectral problem for a periodic elliptic operator with Neumann boundary conditions. More precisely, the corresponding non-selfadjoint secondorder equation is singularly perturbed, each derivative is scaled by ε, the size of the period. The authors prove that the behavior of the first eigenvalue and eigenfunction depends on the fractional part of 1/ε, in contrast to the results obtained in the case of Dirichlet boundary conditions. New asymptotic regimes are obtained for certain values of this fractional part, corresponding to an exponential localization of the first eigenfunction at one of the extreme points of the domain. Reviewed by Dan Polisevsk

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Hypersurfaces in H n and the space of its horospheres. (English summary) Geom. Funct. Anal. 12 (2002), no. 2, 395–435. The author starts with what he calls the “well-known ” duality between convex surfaces in Hn and those in the de Sitter space Sn 1 (to the reviewer’s knowledge, this duality was first exploited in the reviewer’s 1986 doctoral dissertation), and explores a related duality between “H-convex” surfaces in H3 (those which locally lie on one side of a horosphere) and convex surfaces in the space of horospheres in H3, which is a manifold homeomorphic to S2 × R with a degenerate metric of signature (2, 0). The author calls this manifold C3 +. The author completely characterizes those surfaces in C 3 + dual to H-convex surfaces in H 3, and the author’s results extend to surfaces in H n, which is in marked contrast to isometric embedding results (in H ⋉ and Sn 1), where the problem becomes highly overdetermined, and no global characterization is possible

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Hyperbolic manifolds with convex boundary. (English summary

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Classification of polynomials from C 2 to C with one critical value

Reviewed by Arnd Rösch References

Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations. (English summary) SIAM J. Control Optim. 45 (2006), no. 5, 1586–1611 (electronic). The authors study a control constrained semilinear elliptic optimal control problem with Dirichlet boundary control. The domain is assumed to be a convex polygonal set in R 2. The optimal control problem is discretized by piecewise finite elements in control and state. The authors prove as a main result that the approximation order for the discretization is h 1−1/p, which is consistent with the W 1−1/p,p-regularity of the optimal control