Partial Differential Equations

Our research focuses on the following aspects of Partial Differential Equations

  • Optimal Rearrangements, Free boundary Problems, Geometric and Qualitative Properties of the Solutions, Critical Point Theory, Convex and Nonlinear Analysis

  • Free Discontinuity Problems, Regularity at the Crack-Tip/-Front, Variational Crack Propagations Models

  • Material Models for Composites and Metals, Finite Element Method for Stress and Strain Distribution, Continuum Damage and Crystal Plasticity Models

  • A Posteriori Error Estimators for the Approximations Using Finite Element Methods, Guaranteed Upper Bounds on Norm of the Error

  • Non-Linear Evolution Equations, Normalized Standing-Wave Solutions, Models of Stability Problems

  • Mathematical and Theoretical Physics, Quantum Field Theory on Curved Spacetimes, Symmetry breaking in Inflationary Cosmology, Conformal Zero Modes



Group Members




Rencent Publications









Research Group Seminars

First UNNC-XJTLU Joint Mathematical Seminar
Partial Differential Equations Research Group’s Colloquium
Partial Differential Equations Research Group Online Mini Workshop on Application of PDEs in Biology and Medicine
SDE Models and Monte Carlo Simulations in Finance
Partial Differential Equations Research Group Online Mini-Workshop on Mathematical Biology
Partial Differential Equations Research Group Online Mini-Workshop on Nonlinear PDEs
Introduction to Minimal Surfaces
Game theory approach for the analysis of social network structure
On some stationary navier-stokes type problems
Extension of Talenti’s Inequality and Maximum Values Relative to Rearrangement Classes
The Derrida-Retaux model and some mathematical problems
Singular Non-Linear Problems for Monotone Elliptic Operators
Fractional diffusion: From its foundations to some recent open problems