The aim of the Analysis and Partial Differential Equations (PDE) unit is to reveal and analyze the mathematical principles reflecting natural phenomena expressed by partial differential equations. Research focuses on fundamental analysis of PDEs, regularity theory of elliptic and parabolic PDEs, with special emphasis on the regularity of finite boundary points and the point at \(\infty\), its measure-theoretical, probabilistic and topological characterization, well-posedness of PDE problems in domains with non-smooth and non-compact boundaries, global uniqueness, analysis and classification of singularities, asymptotic laws for diffusion processes, regularity theory of nonlinear degenerate and singular elliptic and parabolic PDEs, free boundary problems, optimal control of free boundary systems with distributed parameters. Current areas of interest include Potential Theory, Harmonic Analysis, Probability Theory, Calculus of Variations and Optimal Control, Optimization, Mathematical Biosciences and Quantum Biology. Some of the current research projects in Applied Mathematics include laser ablation of biomedical tissues; preventing aerodynamic stall by in-flight ice accretion in the aerospace industry; cancer detection through Electrical Impedance Tomography and optimal control theory; identification of parameters in large-scale models of systems biology; optimal control of reactive oxygen species in quantum biology.
