Philipp Zimmermann
Postdoctoral
Researcher
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 modelling physical systems exhibiting a nonlocal and nonlinear behaviour 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 main goal here is to better understand the interplay between nonlocal and nonlinear effects in the medium under consideration. These investigations are largely motivated from the observation that nonlinear but also 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.
Selected Papers
On uniqueness in nonlocal diffuse optical tomography (with Y. Lin), Preprint, 2024.
Well-posedness and inverse problems for semilinear nonlocal wave equations (with T. Tyni and Y. Lin), Nonlinear Anal., 247, 113601, 2024.
Unique determination of coefficients and kernel in nonlocal porous medium equations with absorption term (with Y. Lin), Preprint, 2023.
Determining coefficients for a fractional p-Laplace equation from exterior measurements (with M. Kar and Y. Lin), Preprint, 2022.
Inverse problem for a nonlocal diffuse optical tomography equation, Inverse Problems 39 09400, 2023.
The fractional p-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems (with M. Kar and J. Railo), Calc. Var. 62, 130, 2023.
Low regularity theory for the inverse fractional conductivity problem (with J. Railo), Nonlinear Anal., 230, 113418, 2024.