- Matthias Eller (Georgetown University, USA) and
- Daniel Toundykov (University of Nebraska-Lincoln, USA)
Harmonic analysis with applications to uniqueness and inverse estimates for PDE's
Many prominent advances in applied partial differential equations
(PDE's) have emerged alongside landmark developments in functional and
For instance, Carleman-type estimates have been for many decades
indispensable in establishing unique continuation properties and
observability inequalities for problems in PDE control. Pseudo- and
para-differential calculi have been widely employed to investigate
sharp trace regularity in boundary value problems and analyze systems
with irregular coefficients.
Results on Hardy and Triebel-Lizorkin spaces have proved instrumental in study of nonlinear functionals arising in plate theory.
This Minisymposium will gather experts in various areas of harmonic and
functional analysis with applications to the study of partial
differential equations. The discussions of interest will include, but
will not be limited to:
- Uniqueness and stability estimates for solutions of PDE's,
especially with applications to Continuous Observability and Uniform
Stabilization estimates arising in control and inverse problem theory
- Sharp regularity of solutions to PDE's with emphasis on interior and trace regularity in boundary value problems.
- Microlocal regularity of solutions to PDE's and
propagation of singularities with potential applications to localized
- Spectral analysis in the context of control and inverse problems for PDE's.
- Properties of nonlinear functionals arising in various PDE models, e.g. $p$-Laplace or Monge-Ampere equations.
The goal of this program will be to facilitate the state-of-the-art
research on PDE's by sharing and discussing the latest pertinent
advances in various areas of analysis.