By utilizing the properties of , he demonstrated how to handle discontinuities and singularities that naturally occur in physical systems, particularly at corners or endpoints of a boundary. Applications in Mathematical Physics
Muskhelishvili, along with his contemporaries like I. Vekua, established the Georgian school of mathematics, which specialized in the theory of elasticity and the theory of functions of a complex variable. His work was characterized by a relentless pursuit of rigor. Before his interventions, many solutions in elasticity and fracture mechanics relied on intuition or heuristic methods. Muskhelishvili introduced the rigor of complex analysis, turning vague mechanics problems into precise mathematical formulations. By utilizing the properties of , he demonstrated