93 research outputs found
Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary
The main result of the present paper consists in a quantitative estimate of
unique continuation at the boundary for solutions to the wave equation. Such
estimate is the sharp quantitative counterpart of the following strong unique
continuation property: let be a solution to the wave equation that
satisfies an homogeneous Robin condition on a portion of the boundary and
the restriction of on is flat on a segment
with then vanishes in a neighborhood of
Stable Determination of the Discontinuous Conductivity Coefficient of a Parabolic Equation
We deal with the problem of determining a time varying inclusion within a
thermal conductor. In particular we study the continuous dependance of the
inclusion from the Dirichlet-to-Neumann map. Under a priori regularity
assumptions on the unknown defect we establish logarithmic stability estimates.Comment: 36 page
Uniqueness and Lipschitz stability for the identification of Lam\'e parameters from boundary measurements
In this paper we consider the problem of determining an unknown pair
, of piecewise constant Lam\'{e} parameters inside a three
dimensional body from the Dirichlet to Neumann map. We prove uniqueness and
Lipschitz continuous dependence of and from the Dirichlet to
Neumann map
A transmission problem on a polygonal partition: regularity and shape differentiability
We consider a transmission problem on a polygonal partition for the
two-dimensional conductivity equation. For suitable classes of partitions we
establish the exact behaviour of the gradient of solutions in a neighbourhood
of the vertexes of the partition. This allows to prove shape differentiability
of solutions and to establish an explicit formula for the shape derivative
Stability Estimates for an Inverse Hyperbolic Initial Boundary Value Problem with Unknown Boundaries
In this paper we prove stability estimates of logarithmic type for an inverse
problem consisting in the determination of unknown portions of the boundary of
a domain in , from a knowledge, in a finite time observation, of
overdetermined boundary data for initial boundary value problem for anisotropic
wave equation
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