ODEs
First semester / 2nd year undergraduate
Teaching
PDEs
First semester / 3rd year undergraduate
Resources: Prof. C. Lefter's page
PDE's Companion - Plan for problem sessions - work in progress
A student's notes to use as a guide.
Functional Analysis
Second semester / 3rd year undergraduate
Functional Analysis' Companion - Plan for problem sessions - work in progress
Complex Analysis and Applications
Second semester / 2nd year undergraduate
Resources: Complex Analysis' page
Research
Reaction-diffusion systems in annular domains: source stability estimates with boundary observations
CG Lefter, EA Melnig
Optimization, 1–34, 2024. https://doi.org/10.1080/02331934.2024.2444618
𝐿q-Carleman estimates with boundary observations and applications to inverse problems
EA Melnig
Preprint arXiv:2311.15692, 2023
Internal Controllability of Parabolic Systems with Star-and Tree-like Couplings
CG Lefter, EA Melnig
SIAM Journal on Control and Optimization 60 (5), 3100-3126, 2022
Stability in inverse source problems for nonlinear reaction–diffusion systems
EA Melnig
Nonlinear Differential Equations and Applications NoDEA 28 (4), 45, 2021
Internal feedback stabilization for parabolic systems coupled in zero or first order terms
EA Melnig
Evolution Equations & Control Theory 10 (2), 2021
Stability in 𝐿𝑞-norm for inverse source parabolic problems
EA Melnig
Journal of Inverse and Ill-posed Problems 28 (6), 797-814, 2020
On the parabolic regularity, Sobolev embeddings and global Carleman estimates in 𝐿q(𝐿p) spaces
CG Lefter, EA Melnig
Pure Appl. Funct. Anal. 5, No. 5, 1095--1113, 2020
Feedback stabilization with one simultaneous control for systems of parabolic equations
CG Lefter, EA Melnig
Math. Control Relat. Fields 8 (3-4), 777-787, 2018