Research

RESEARCH INTERESTS:

Partial Differential Equations
Calculus of Variations
Stochastic PDEs
Applied Analysis
Functional inequalities of type Hardy-Sobolev-Rellich, Caffarelli-Kohn-Nirenberg.

Research publications/preprints

K. Tzirakis, Improving interpolated Hardy and trace Hardy inequalities on bounded domains, Nonlinear Analysis 127 (2015), 17-34.
K. Tzirakis, Sharp trace Hardy-Sobolev inequalities and fractional Hardy-Sobolev inequalities, Journal of Functional Analysis 270 (2016), 4513-4539.
D.C. Antonopoulou, G. Karali, K. Tzirakis, Layer dynamics for the one dimensional ε-dependent Cahn-Hilliard/Allen-Cahn equation, (preprint on arXiv) , Calc. Var. 60, 207 (2021).
K. Tzirakis, Series expansion of weighted Finsler-Kato-Hardy inequalities, Nonlinear Analysis, Volume 222, 2022, 113016.
K. Tzirakis, “Weighted trace Hardy inequalities with sharp remainder terms”, Proceedings of 15th Panhellenic Conference of Mathematical Analysis, 2016.
K. Tzirakis, “Caffarelli-Kohn-Nirenberg inequalities on homogeneous Lie groups”, submitted 2023.
D.C. Antonopoulou, G. Dewhirst, G. Karali, K. Tzirakis, “Local existence of the outer parabolic stochastic Stefan problem on the sphere”, submitted 2023.
K. Tzirakis, Stability estimates for fractional Hardy-Schrödinger operators, Chapter: Fixed Point Theory and Chaos (open access, peer-reviewed book), 2023, ISBN 978-1-83768-436-6.
K. Tzirakis, “Optimal Hardy-Sobolev estimates for fractional Hardy-Schrödinger operators on bounded domains”, preprint 2021.
K. Tzirakis, “Interpolated Hardy-trace Hardy weighted inequalities for anisotropic Laplacian, with sharp Hardy-Sobolev type improvements”, preprint 2021.

On going projects

Dynamics of FitzHugh-Nagumo Equations on Warped Cylinders.
- In collaboration with Professor I.M. Sigal, Department of Mathematics, University of Toronto, Canada.
- Funded by Hellenic Foundation for Research and Innovation (H.F.R.I.) – “Basic research financing”, Principal Investigator: G. Karali, Department of Mathematics and Applied Mathematics, University of Crete.
Multi-dimensional fractional-stochastic Stefan problem.
- Funded by Hellenic Foundation for Research and Innovation (H.F.R.I.) – “Basic research financing”, Interfacial phenomena in stochastic reaction-diffusion systems and applications to mathematical finance, IPMAFIN.
- Principal Investigator: G. Karali, Department of Mathematics and Applied Mathematics, University of Crete.