220 research outputs found
Strong unique continuation for general elliptic equations in 2D
We prove that solutions to elliptic equations in two variables in divergence
form, possibly non-selfadjoint and with lower order terms, satisfy the strong
unique continuation property.Comment: 10 page
Single-logarithmic stability for the Calder\'on problem with local data
We prove an optimal stability estimate for Electrical Impedance Tomography
with local data, in the case when the conductivity is precisely known on a
neighborhood of the boundary. The main novelty here is that we provide a rather
general method which enables to obtain the H\"older dependence of a global
Dirichlet to Neumann map from a local one on a larger domain when, in the layer
between the two boundaries, the coefficient is known.Comment: 12 page
Corrigendum to ``Determining a sound-soft polyhedral scatterer by a single far-field measurement''
In the paper, G. Alessandrini and L. Rondi, ``Determining a sound-soft
polyhedral scatterer by a single far-field measurement'', Proc. Amer. Math.
Soc. 133 (2005), pp. 1685-1691, on the determination of a sound-soft polyhedral
scatterer by a single far-field measurement, the proof of Proposition 3.2 is
incomplete. In this corrigendum we provide a new proof of the same proposition
which fills the previous gap.Comment: 3 page
Cracks with impedance, stable determination from boundary data
We discuss the inverse problem of determining the possible presence of an
(n-1)-dimensional crack \Sigma in an n-dimensional body \Omega with n > 2 when
the so-called Dirichlet-to-Neumann map is given on the boundary of \Omega. In
combination with quantitative unique continuation techniques, an optimal
single-logarithm stability estimate is proven by using the singular solutions
method. Our arguments also apply when the Neumann-to-Dirichlet map or the local
versions of the D-N and the N-D map are available.Comment: 40 pages, submitte
Quantitative estimates on Jacobians for hybrid inverse problems
We consider -harmonic mappings, that is mappings whose components
solve a divergence structure elliptic equation , for . We investigate whether, with suitably prescribed
Dirichlet data, the Jacobian determinant can be bounded away from zero. Results
of this sort are required in the treatment of the so-called hybrid inverse
problems, and also in the field of homogenization studying bounds for the
effective properties of composite materials.Comment: 15 pages, submitte
Determining the anisotropic traction state in a membrane by boundary measurements
We prove uniqueness and stability for an inverse boundary problem associated
to an anisotropic elliptic equation arising in the modeling of prestressed
elastic membranes.Comment: 6 page
Invertible harmonic mappings, beyond Kneser
We prove necessary and sufficient criteria of invertibility for planar
harmonic mappings which generalize a classical result of H. Kneser, also known
as the Rad\'{o}-Kneser-Choquet theorem.Comment: One section added. 15 page
Estimates for the dilatation of -harmonic mappings
We consider planar -harmonic mappings, that is mappings whose
components and solve a divergence structure elliptic equation , for . We investigate whether a locally
invertible -harmonic mapping is also quasiconformal. Under mild
regularity assumptions, only involving and the antisymmetric part
of , we prove quantitative bounds which imply quasiconformality.Comment: 8 pages, to appear on Rendiconti di Matematica e delle sue
applicazion
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