Research
Theoretical and applied analysis of multiscale PDEs and complex domains.
Research interests
- Partial Differential Equations
- Homogenization
- Calculus of Variations
- Optimal Control
- Spectral Theory
- Asymptotic Analysis
- Thin Domains
- Oscillating Domains
- Dimension Reduction
- Multiscale Analysis
Current directions
Current interests include spectral problems with indefinite weights, thin and oscillating media, locally periodic structures, nonlinear PDEs, Steklov problems and higher-order operators.
A recent project studies how sign-changing spectral densities affect positive and negative spectrum under thin-domain limits.
Research themes
Homogenization
Effective behaviour of PDEs in rapidly varying coefficients and geometrically oscillating domains.
Spectral asymptotics
Convergence and localization of eigenvalues/eigenfunctions in thin and multiscale structures.
Optimal control
Asymptotic analysis of control problems posed on rough and oscillating domains.