Detection of an unknown domain and related topics

Project leaders

Gabriele Inglese, Jenn-nan Wang

Agreement

TAIWAN - NSTC - National Science and Technology Council

Call

CNR/NSC 2012-2013

Department

Earth and Environment

Thematic area

Earth system science and environmental technologies

Status of the project

New

Research proposal

The theme of this proposal is to investigate the identification of
unknown domain and related questions in different settings. One of
the main tools for the proposed problem is the quantitative estimate
of the unique continuation property for the solutions of the
corresponding equations. The quantitative estimate of the unique
continuation property itself is an interesting question and has many
applications to other problems besides of inverse problems. In this
project, we will mostly focus on the system of equations. To be
precise, we consider the shallow shell equations and the
Maxwell equations with anisotropic media. For other problems, we
also consider the Helmholtz equation and the conductivity equation
with discontinuous coefficient.

Research goals

1    Detection in the shallow shell equations
1.1  Size estimate
1.2  Uniqueness and stability of determining unknown boundaries in the shallow shell equations
2    Stability estimate of determining an inclusion in the Maxwell equations
3    Size estimate in the Helmholtz equation
4    Quantitative uniqueness estimates for equations with non-smooth coefficients

Last update: 08/06/2025