Davit(David) Harutyunyan

Assistant Professor

University California Santa Barbara
Department of Mathematics

Office: South Hall 6504
email: harutyunyan(at)math(dot)ucsb(dot)edu

Research Interests (Applied Analysis)
  • Analysis of Partial Differential Equations and Calculus of Variations
  • Continuum Mechanics (Elasticity)
  • Composite Materials, Metamaterials, Materials Science
  • Micromagnetics
    My research is partially supported by the NSF DMS grant 1814361

  • Short Bio

    I did my Ph.D. (degree received in 2012) at Hausdorff Center for Mathematics under the supervision of Prof. Stefan Mueller. Before joining the UCSB, I held postdoctoral positions at Temple University (with Prof. Yury Grabovsky), University of Utah (with Prof. Graeme Milton) and EPFL (with Prof. Hoai-Minh Nguyen). Here is my (updated 06.2020) CV

    Publications and preprints

    33. D. Harutyunyan. On the L^2 to L^p passage in sharp geometric rigidity estimates and korn inequalities in thin domains. In preparation (2021).
    32. D. Harutyunyan and H. Mikayelyan. Fractional Hardy and Korn inequalities in simplexes. In preparation (2021).
    31. D. Harutyunyan and Andre Martins Rodrigues. The buckling load in the buckling of convex cilindrical shells under vertical compression depends on the curvature of the cross section. In preparation (2021).
    30. D. Harutyunyan. A hint on the localization of the buckling deformation at vanishing curvature points on thin elliptic shells. Submitted (2021). 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. Submitted (2021). 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., 16th February, 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


  • Summer of 2020: Math 108B. syllabus