In my research I am using techniques from the Calculus of Variations and from the Theory of Partial Differential Equations to answer questions arising from continuum mechanics ( both dynamics and statics) and image analysis. Some of my research topics are:
Weak-strong uniqueness under quasiconvexity conditions
Variational schemes for hyperbolic PDEs
Discontinuous Galerkin methods for nonlinear variational problems
Quasistatic evolution problems and rate independent processes
Convexity properties of interfacial energies
Bilevel training schemes for image reconstruction
Publications/Preprints:
A-quasiconvexity, Gårding inequalities, and applications in PDE constrained problems in dynamics and statics. SIAM Journal on Mathematical Analysis, (2021) with Konstantinos Koumatos (link)
Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity. Comm. Partial Differential Equations, (2022) with Myrto Galanopoulou and Konstantinos Koumatos (link)
Bilevel training schemes in imaging for total-variation-type functionals with convex integrands, SIAM Journal of Imaging Sciences, (2021) with Valerio Pagliari, Kostas Papafitsoros and Bogdan Raita (link)
A class of Discontinuous Galerkin methods for nonlinear variational problems, accepted Math. Comp. (2024), with Georgios Grekas, Charalambos Makridakis and Konstantinos Koumatos (link)
Quasistatic nonassociative plasticity at finite strains, submitted (2024), with Ulisse Stefanelli (link)
Work in progress:
Measure-valued solutions for non-associative finite plasticity, with Ulisse Stefanelli
DG methods for non-convex nonlinear variational problems, with Georgios Grekas, Charalambos Makridakis and Konstantinos Koumatos
Variational principles for thermodynamics out of equilibrium, with Myrto Galanopoulou, Konstantinos Koumatos and Athanasios Tzavaras
Necessary and sufficient conditions for interface quasiconvexity, with Martin Horák and Martin Kružík