IFIP TC 7 / 2013 - Minisymposia

  • 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 harmonic analysis.
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 for PDE's.
  • 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 control mechanisms.
  • 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.