Professor of Mathematics
Department of Mathematics
Temple University
1805 North Broad Street
Philadelphia,
PA 19122-6094
email: yury at temple dot edu
Phone: (215) 204-1650
Fax: (215) 204-6433
Grabovsky, Y. The G-closure of two well-ordered anisotropic conductors, Proc. Royal Society of Edinburgh, 123A, pp. 423-432, 1993. final publication, pdf file.
Grabovsky, Y. and Kohn, R. V. Microstructures minimizing the energy of a two phase composite in two space dimensions. I: The confocal ellipse construction, J. Mech. Phys. Solids, 43, No. 6, pp. 933-947, 1995. final publication, pdf file.
Grabovsky, Y. and Kohn, R. V. Microstructures minimizing the energy of a two phase composite in two space dimensions. II: The Vigdergauz microstructure, J. Mech. Phys. Solids, 43, No. 6, pp. 949-972, 1995. final publication, pdf file.
Grabovsky, Y. Nonsmooth analysis and quasi-convexification in elastic energy minimization problems, Structural Optimization, 10, pp. 217-221, 1995. final publication, pdf file.
Grabovsky, Y. and Kohn, R. V. Anisotropy of the Vigdergauz microstructure, J. Appl. Mech.,62, No. 4, pp. 1063-1065, 1995. final publication,
Grabovsky, Y. Bounds and extremal microstructures for two-component composites: A unified treatment based on the translation method, Proc. Roy. Soc. London, 452A, pp. 919-944, 1996. final publication, pdf file.
Grabovsky, Y. Explicit solution of an optimal design problem with non-affine displacement boundary conditions, Proc. Roy. Soc. London, 452A, pp. 909-918, 1996. final publication, pdf file.
Grabovsky, Y. and Milton, G. W., Rank one plus a null-Lagrangian is an inherited property of two-dimensional compliance tensors under homogenization, Proc. Roy. Soc. Edinburgh., 128A, pp. 283-299, 1998. final publication, pdf file
Cherkaev, A. V., Grabovsky, Y., Movchan, A. B. and Serkov, S. K. Optimality of dilute composites under shear load, in "IUTAM Symposium on Transformation Problems in Composite and Active Materials" Proceedings of the IUTAM Symposium held in Cairo, Egypt, 9-12 March 1997 G. M. L. Gladwell, Yehia A., Y. A. Bahei-el-Din and G. J. Dvorak, eds., pp. 285-300, Springer Netherlands, 2002. final publication.
Cherkaev, A. V., Grabovsky, Y., Movchan, A. B. and Serkov, S. K. The cavity of the optimal shape under shear stresses, Int. J. Solids Struct., 35, No. 33, pp. 4391-4410, 1998. final publication.
Grabovsky, Y. and Milton, G. W., Exact Relations for Composites: Towards a Complete Solution, Doc. Math. J. DMV Extra Volume ICM III, pp. 623-632, 1998.
Grabovsky, Y., Exact relations for effective tensors of polycrystals. I: Necessary conditions, Arch. Rat. Mech. Anal., 143, No. 4, pp. 309-329, 1998. final publication, pdf file
Grabovsky, Y. and Sage, D. S., Exact relations for effective tensors of polycrystals. II: Applications to elasticity and piezo-electricity, Arch. Rat. Mech. Anal., 143, No. 4, pp. 331-356, 1998. final publication, pdf file
Grabovsky, Y., Milton, G. W. and Sage, D. S., Exact relations for effective tensors of polycrystals: Necessary conditions and sufficient conditions, Comm. Pure Appl. Math., 53, No. 3, pp. 300-353, 2000. final publication, pdf file. Here is a short summary of the paper.
Grabovsky, Y. Optimal design problems for two-phase conducting composites with weakly discontinuous objective functionals, Advances in Applied Mathematics, 27, pp. 683-704, 2001. final publication, pdf file
Grabovsky, Y. Homogenization in an optimal design problem with weakly discontinuous objective functional, Int. J. Diff. Eq. Appl., 3, No. 2, pp. 183-194, 2001. pdf file
Grabovsky, Y. Algebra, geometry and computations of exact relations for effective moduli of composites in Advances in Multifield Theories of Continua with Substructure, Capriz and Mariano, eds., 167-197, Model. Simul. Sci. Eng. Technol., Birkhäuser Boston, Boston, MA, 2004. final publication, pdf file.
Grabovsky, Y. and Hijab, O. A generalization of the Chandler Davis convexity theorem, Adv. Appl. Math., 34, No. 1, pp. 192-212, 2005. final publication, pdf file
Grabovsky, Y. and Mengesha, T. Direct approach to the problem of strong local minima in Calculus of Variations, Calculus of Variations and PDE, 29, No. 1, pp. 59-83, 2007. final publication, pdf file, erratum
Grabovsky, Y. and Truskinovsky, L. The flip side of buckling, Continuum Mechanics and Thermodynamics, 19, No. 3-4, pp. 211-243, 2007. final publication, pdf file.
Grabovsky, Y. and Mengesha, T. Sufficient conditions for strong local minima: the case of C^1 extremals. Transactions of the AMS, 361, No. 3, pp. 1495–1541, 2009. final publication, pdf file.
Grabovsky, Y. An application of the general theory of exact relations to fiber-reinforced conducting composites with Hall effect. Mechanics of Materials. 41, No. 4, pp. 456-462, 2009. final publication, pdf file.
Grabovsky, Y. Exact relations for effective conductivity of fiber reinforced conducting composites with Hall effect via a general theory. SIAM J. Math. Anal. 41, No. 3, pp. 973-1024, 2009. final publication, pdf file.
Grabovsky, Y., Kucher, V. A. and Truskinovsky, L. Weak variations of Lipschitz graphs and stability of phase boundaries. Continuum Mechanics and Thermodynamics, 23, No. 2, pp. 87-123, 2011. final publication, pdf file.
Grabovsky, Y. and Truskinovsky, L. Roughening instability of broken extremals. Archive for Rational Mechanics and Analysis, 200, No. 1, pp. 183-202, 2011. final publication, pdf file.
Grabovsky, Y. and Truskinovsky, L. Marginal material stability. Journal of Nonlinear Science, 23, No. 5, pp. 891-969, 2013. final publication, pdf file.
Grabovsky, Y. and Truskinovsky, L. Normality condition in elasticity. Journal of Nonlinear Science, 24, No. 6, pp. 1125-1146, 2014. final publication, pdf file.
Grabovsky, Y. and Harutyunyan, D. Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells SIAM J. Math. Anal., 46, No. 5, pp. 3277-3295, 2014. final publication, pdf file.
Grabovsky, Y. and Harutyunyan, D. Rigorous derivation of the formula for the buckling load in axially compressed circular cylindrical shells J. Elasticity, 120, No. 2, pp. 249-276, 2015. final publication, pdf file.
Grabovsky, Y. and Harutyunyan, D. Scaling instability of the buckling load in axially compressed cylindrical shells Journal of Nonlinear Science, 26, No. 1, pp. 83-119, 2016. final publication, pdf file.
Grabovsky, Y. and Truskinovsky, L. Legendre-Hadamard conditions for two-phase configurations. J. Elasticity, 123, No. 2, pp. 225-243, 2016. final publication, pdf file.
Grabovsky, Y. Composite materials: Mathematical theory and exact relations. IOP Publishing Ltd 2016, Online ISBN: 978-0-7503-1048-2, Print ISBN: 978-0-7503-1049-9.
Bitew, W. T. and Grabovsky, Y. Higher regularity of uniform local minimzers in Calculus of Variations. Proceedings of the AMS,145, No. 12, pp. 5215-5222, 2017. final publication, pdf file.
Grabovsky, Y. and Harutyunyan, D. Korn inequalities for shells with zero Gaussian curvature. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 35, No. 1, pp. 267-282, 2018. final publication, pdf file.
Grabovsky, Y. From microstructure-independent formulas for composite materials to rank-one convex, non-quasiconvex functions. Archive for Rational Mechanics and Analysis,227, No. 2, pp. 607–636, 2018. final publication, full-text view-only version, pdf file.
Grabovsky, Y. and Truskinovsky, L. When rank one convexity meets polyconvexity: an algebraic approach to elastic binodal. preprint.
On February 29, 2000 I gave a "Leap Lecture" to undergraduates in Temple University. The Portuguese translation of this lecture appears in Educacao e Matematica, 89, pp. 82-88, 2006.