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 a proof of Ball's conjecture in the Calculus of Variations and mathematical analysis of buckling of slender elastic bodies, such as plates rods and shells.