## Computational and Applied Mathematics Seminar

**Spring 2017**

**Mondays at 4:10 p.m. in 401 Carver
**

The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.

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2/13

**Calderón-Zygmund estimates for parabolic equations**

**Pablo Raúl Stinga
**Iowa State University

**Abstract:** We show how to use the language of semigroups in combination with the general Calderón—Zygmund theory on spaces of homogeneous type to obtain (weighted) Sobolev estimates for parabolic equations. One of the main features of this point of view is that it avoids the heavy use of the symmetries of the Fourier transform. Instead, our method takes advantage of semigroup kernel estimates. In this way we can prove novel estimates for non-translation invariant equations as well as for equations with bounded measurable time-dependent coefficients. We finally present some new (weighted) mixed-norm Sobolev estimates in the spirit of N. V. Krylov

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2/13

**Calderón-Zygmund estimates for parabolic equations**

**Pablo Raúl Stinga
**Iowa State University

**Abstract:** We show how to use the language of semigroups in combination with the general Calderón—Zygmund theory on spaces of homogeneous type to obtain (weighted) Sobolev estimates for parabolic equations. One of the main features of this point of view is that it avoids the heavy use of the symmetries of the Fourier transform. Instead, our method takes advantage of semigroup kernel estimates. In this way we can prove novel estimates for non-translation invariant equations as well as for equations with bounded measurable time-dependent coefficients. We finally present some new (weighted) mixed-norm Sobolev estimates in the spirit of N. V. Krylov

2/20

**Identification of an inclusion in multifrequency electrical impedance tomography**

**Faouzi Triki **

University of Grenoble, Alpes

**Abstract:** In the talk I will present recent results on multifrequency electrical impedance tomography. The inverse problem consists in identifying a conductivity inclusion inside a homogeneous background medium by injecting one current. I will use an original spectral decomposition of the solution of the forward conductivity problem to retrieve the Cauchy data corresponding to the extreme case of perfect conductor. Considering results based on the unique continuation I will then prove the uniqueness of the multifrequency electrical impedance tomography and obtain rigorous stability estimates. Finally, I will present numerical results inspired by the developed theoretical approach. This work has been done in collaboration with Habib Ammari (ETH Zürich,Switzerland) and Chun-Hsiang Tsou (Grenoble Alpes University)