Yury Grabovsky

Associate Professor.

ADDRESS

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

Publications/Preprints

• Grabovsky, Y. The G-closure of two well-ordered anisotropic conductors, Proc. Royal Society of Edinburgh, 123A, pp. 423-432, 1993. 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, pp. 1063-1065, 1995.

• 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. 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. 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.

• Bitew, W. T. and Grabovsky, Y. Higher regularity of uniform local minimzers in Calculus of Variations.    Submitted. pdf file.

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.

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