Philipp Zimmermann

Contact Information

Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona,Spain

E-Mail: philipp.zimmermann@ub.edu

OrcID: https://orcid.org/0000-0002-6791-1779 

Google Scholar ID: https://scholar.google.com/citations?user=YiJXYVoAAAAJ 

About Me

I am a postdoctoral researcher at the Departament de Matemàtiques i Informàtica, Universitat de Barcelona in Spain. My research focuses on local and nonlocal partial differential equations (PDEs), inverse problems and free boundary problems. 

In my recent research projects, I mainly studied PDEs modeling physical systems exhibiting a nonlocal and nonlinear behavior like the fractional p-Laplace equation, fractional p-biharmonic systems, nonlocal porous medium equations or semilinear nonlocal wave equations. In these works a special emphasis is put on the related inverse problems. The principal goal here is to understand better the interplay between nonlocal and nonlinear effects in the medium under consideration. These investigations are largely motivated by the observation that nonlinear or nonlocal operators in different settings support the unique determination of the physical quantities of interest.

Furthermore, another goal of my research is the use of nonlocal techniques to study inverse problem for local PDEs. In particular, I showed together with my collaborators in [1] that the metric and potential appearing in a Schrödinger equation posed in a transversally anisotropic geometry are uniquely determined by the Neumann to Dirichlet map.

Selected Papers

1. Optimal Runge approximation for damped nonlocal wave equations and simultaneous determination results, Preprint, 2024.

2. Well-posedness and inverse problems for semilinear nonlocal wave equations (with T. Tyni and Y. Lin), Nonlinear Anal., 247, 113601, 2024.

3. The Calderón problem for the Schrödinger equation in transversally anisotropic geometries with partial data (with G. Nakamura, Y. Lin), Preprint, 2024.

4. Approximation and uniqueness results for the nonlocal diffuse optical tomography problem (with Y. Lin), Preprint, 2024.

5. Unique determination of coefficients and kernel in nonlocal porous medium equations with absorption term (with Y. Lin), Preprint, 2023. 

6. Inverse problem for a nonlocal diffuse optical tomography equation, Inverse Problems 39 09400, 2023.

7. The fractional p-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems (with M. Kar and J. Railo), Calc. Var. 62, 130, 2023.

8. Low regularity theory for the inverse fractional conductivity problem (with J. Railo), Nonlinear Anal., 230, 113418, 2024.