Davit(David) Harutyunyan

Associate Professor

University California Santa Barbara
Department of Mathematics

Office: South Hall 6515
email: harutyunyan(at)math(dot)ucsb(dot)edu

Research Interests: Applied Analysis (Materials Science)

My research is partially supported by NSF DMS Grant 2206239 (2022-2025)
Previously supported by NSF DMS Grant 1814361 (2018-2022)

Here is my (updated 01.2023) CV

Publications and preprints

34. D. Harutyunyan. On the L^2 to L^p passage in sharp geometric rigidity estimates and korn inequalities in thin domains. In preparation (2022).
33. D. Harutyunyan, H. Mikayelyan, T. Mengesha, and J. Scott. Fractional Korn's inequalities without boundary conditions. submitted, 2023. arxiv
32. D. Harutyunyan and H. Mikayelyan. On the fractional Korn inequality in bounded domains: Counterexamples to the case ps<1. Advances in Ninlinear Analysis, Frbruary 27, 2023. online arxiv
31. D. Harutyunyan and Andre Martins Rodrigues. The buckling load of cylindrical shells under axial compression depends on the cross-section curvature. Journal of Nonlinear Science, 33: 27 (2023). online arxiv
30. D. Harutyunyan. A hint on the localization of the buckling deformation at vanishing curvature points on thin elliptic shells. Journal of Elasticity 152 , pp. 61–77 (2022) online arxiv
29. D. Harutyunyan and N. Hovsepyan. On the extreme rays of the cone of 3 times 3 quasiconvex quadratic forms: Extremal determinats vs extremal and polyconvex forms. Arch. Ration. Mech. Anal., 244 , pp. 1–25 (2022) online arxiv
28. Zh. Avetisyan, D. Harutyunyan, and N. Hovsepyan. Rigidity of a thin domain depends on the curvature, width, and boundary conditions. Appl. Math. Optim., Vol. 84, pp. 3229-3254 (2021). online arxiv
27. D. Harutyunyan. On the geomatric rigidity interpolation estimate in thin bi-Lipschitz domains. C. R. Math. Acad. Sci. Paris, 358 (2020) no. 7, pp. 811-816. online
26. D. Harutyunyan. The sharp L^p Korn interpolation and second inequalities in thin domains. SIAM J. Math. Anal., 52(6), 5775-5791, 2020. online arxiv
25. D. Harutyunyan. The asymptotically sharp geomatric rigidity interpolation inequality in thin bi-Lipschitz domains. Journal of Elasticity, 141, pp. 291-300 (2020), online arxiv
24. D. Harutyunyan and H. Mikayelyan. On the L-infinity maximization of the solution of Poisson's equation: Brezis-Galouet-Wainger type inequalities and applications, Proc. Roy. Soc. Edinburgh A, Published online: 20 February 2020. DOI: https://doi.org/10.1017/prm.2020.3 arxiv
23. D. Harutyunyan. A note on the extreme points of the cone of quasiconvex quadratic forms with orthotropic symmetry. Journal of Elasticity, 09 January, 2020, pp. 1-15. online arxiv
22. D. Harutyunyan and H. Mikayelyan. Weighted asymptotic Korn and interpolation Korn inequalities with singular weights. Proceedings of the AMS, 147 (2019), pp. 3635-3647. online arxiv
21. D. Harutyunyan. On the Korn interpolation and second inequalities in thin domains, SIAM J. Math. Anal., Vol. 50, Iss. 5, 2018, pp. 4964-4982. online arxiv
20. D. Harutyunyan. The asymptotically sharp Korn interpolation and second inequalities for shells. C. R. Math. Acad. Sci. Paris, Vol. 356, Iss. 5, 2018, pp. 575-580. online arxiv
19. D. Harutyunyan. When the Cauchy inequality becomes a formula. Amer. Math. Month. , 125:9, pp. 835-838, 2018. online arxiv
18. G.W.Milton, D. Harutyunyan and M. Briane. Towards a complete characterization of effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase. Math. Mech. Compl. Sys., 5(1), 95-113, 2017. online arxiv
17. G.W.Milton, M. Briane and D. Harutyunyan. On the possible effective elasticity tensors of 2-dimensinal and 3-dimensional printed materials. Math. Mech. Compl. Sys., Vol. 5, No. 1, 41-94, 2017. online arxiv
16. D. Harutyunyan. Quantitative anisotropic isoperimetric and Brunn-Minkowski inequalities for convex sets with improved defect estimates. ESAIM: COCV, . 24 (2018) 479-494. online arxiv
15. D. Harutyunyan. Gaussian curvature as an identifier of shell rigidity. Arch. Ration. Mech. Anal., Nov. 2017, Vol. 226, Iss. 2, pp. 743-766 online arxiv
14. Y.Grabovsky and D. Harutyunyan. Korn inequalities for shells with zero Gaussian curvature. Ann. d'Inst. Henri Poincare (C), Nonl. Anal.. 2018, Vol. 35, Iss. 1, pp. 267-282. online, arxiv
13. D. Harutyunyan, G.W.Milton and R.V.Craster. High frequency homogenization for travelling waves in periodic media, Proc. Roy. Soc. London A, 2016, online , arxiv
12. D. Harutyunyan. Sharp weighted Korn and Korn-like inequalities and an application to washers. Journal of Elascitiy, Vol. 127, Iss. 1, pp. 59-77, 2017. online arxiv
11. D. Harutyunyan and G.W.Milton. Towards characterization of all 3\times 3 extremal quasiconevex quadratic forms, Comm. Pure Appl. Math., Vol. 70, Issue 11, Nov. 2017, pp. 2164-2190. online, arxiv
10. D. Harutyunyan, G.W.Milton, T.J. Dick and J.Boyer. On ideal dynamic climbing ropes, Proc. Inst. Mech. Eng., Part P: J. Sports Eng. Tech., , 2016. online DOI: 10.1177/1754337116653539
9. D. Harutyunyan and G.W.Milton. On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials, Arch. Ration. Mech. Anal., Vol. 223, Iss. 1, pp 199-212, 2017. online, arxiv
8. Y.Grabovsky and D. Harutyunyan. Scaling intability in buckling of axially compressed cylindrical shells. Journal of Nonlinear Science , Vol. 26, Iss. 1, pp. 83-119, Feb. 2016. online, arxiv
7. D. Harutyunyan. On the existence and stability of minimizers in ferromagnetic nanowires. J. Math. Anal. Appl., 2015. Vol. 434, Iss. 2, pp. 1719-1739. 15 Feb. 2016. online, arxiv
6. D. Harutyunyan and G.W.Milton. Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex. Calc. Var. PDE , October 2015, Volume 54, Issue 2, pp. 1575-1589. online , arxiv
5. Y.Grabovsky and D. Harutyunyan. Rigurous derivation of the formula for the buckling load in axially compressed circular cylindrical shells. Journal of Elasticity, 120(2), pp. 249-276, 2015. .online, arxiv
4. D. Harutyunyan. New asymptotically sharp Korn and Korn-like inequalities in thin domains. Journal of Elasticity, 117(1), pp. 95-109, 2014. online , arxiv
3. Y.Grabovsky and D. Harutyunyan. Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells. SIAM J. Math. Anal. . 46(5), pp. 3277-3295, 2014 .online, arxiv.
2. D. Harutyunyan. Scaling laws and the rate of convergence in magnetic thin films. J. Math. Anal. Appl., 420(2), pp. 1744-1761, 2014.online, arxiv
1. D. Harutyunyan. On the number of arrangements of n-ary brackets , Lomonosov 2002 proceedings, Moscow State University, 2002.
  • [Ph.D. Thesis] D. Harutyunyan. On the G-convergence of the energies and the convergence of almost minimizers in infinite magnetic cylinders, Dissertation: Universitaets und Landesbibliothek Bonn, 2012, online


  • Winter of 2023: Introduction to Real Analysis (Math 201B). syllabus