Yury Grabovsky's interests are in the area of Calculus of Variations, PDE, and applications to Continuum Mechanics. He has worked on the mathematical theory of composite materials, non-linear elasticity, and phase transitions in solids. His work on exact relations for effective tensors of polycrystalline composites has combined methods of modern algebra and PDE. His recent work includes mathematical analysis of buckling of slender elastic bodies, such as plates rods and shells, study of feasibility of extrapolation of special classes of functions, such as Stieltjes and completely monotone functions and algorithms for their optimal reconstruction.