Article

The linear constraints in Poincar\'{e} and Korn type inequalities

01/2006; DOI:10.1515/FORUM.2008.028
Source: arXiv

ABSTRACT We investigate the character of the linear constraints which are needed for Poincar\'e and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a portion of the boundary. Comment: Revised version

0 0
 · 
0 Bookmarks
 · 
76 Views
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier-Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log-log type.
    Applicable Analysis. 03/2011;
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: For a bounded three-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first inequality. On the other hand, for skew-symmetric tensor fields our new estimate turns to Poincare's inequality. Therefore, our result may be viewed as a natural common generalization of Korn's first and Poincare's inequality. Decisive tools for this unexpected estimate are the classical Korn's first inequality, Helmholtz decompositions for mixed boundary conditions and the Maxwell estimate.
    03/2012;
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of results concerns uniqueness and stability for the determination of unknown boundaries, including the cases of cavities and rigid inclusions. In the second group of results, we consider upper and lower estimates of the area of unknown inclusions given in terms of the work exerted by a couple field applied at the boundary of the plate. In particular, we extend previous size estimates for elastic inclusions to the case of cavities and rigid inclusions. Key words: inverse problems, elastic plates, uniqueness, stability estimates, size estimates, three sphere inequality, unique continuation.
    09/2012;

Full-text (2 Sources)

View
17 Downloads
Available from
Jan 29, 2013