[30] A. Lemenant and M.R. Pakzad, The biharmonic optimal support problem, Preprint, (2024).
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[29] M.R. Pakzad, Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature, Preprint, (2022).
PDF
[28] S. Li, M.R. Pakzad and A. Schikorra, Fractional Sobolev isometric immersions of planar domains,
Preprint, (2021), to appear in Ann. Sc. Norm. Sup. Pisa - Classe di Scienze.
PDF
[27] C. De Lellis and M.R. Pakzad, The geometry of $C^{1,\alpha}$ flat isometric immersions,
Preprint, (2020), to appear in Proc. A Royal Soc. Edinburgh.
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[26] Z. Liu, J. Maly and M.R. Pakzad, Approximation by mappings with singular Hessian minors,
Nonlinear Anal. 176, 209--225, (2018).
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[25] P. Goldstein, P. Hajlasz and M.R. Pakzad, Finite Distortion Sobolev Mappings between Manifolds are Continuous,
International Mathematics Research Notices, Volume 2019, Issue 14, Pages 4370--4391, (July 2019).
PDF
[24] R.L. Jerrard and M.R. Pakzad, Sobolev Spaces of isometric immersions of arbitrary dimension and co-dimension,
Ann. Mat. Pura Appl. (4), 196, no. 2, 687--716, (2017).
PDF
[23] M. Lewicka and M.R. Pakzad, Convex integration for the Monge-Ampère equation in two dimensions,
Analysis and PDE, Vol. 10, No. 3, 695--727, (2017).
PDF
Erratum
[22] M. Lewicka, L. Mahadevan and M.R. Pakzad,
The Monge-Ampère constraint: matching of isometries, density and
regularity, and elastic theories of shallow shells,
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol 34, Issue 1, 45--67, (2017).
Older Version PDF
New Version PDF
[21] M. Lewicka and M.R. Pakzad,
Prestrained elasticity: from shape formation to Monge-Ampère anomalies,
Notices of the AMS, vol 63, no. 1, (January 2016).
PDF
Longer Version
[20] A. Acharya, M. Lewicka and M.R. Pakzad, The metric restricted inverse design problem,
Nonlinearity, Vol 29, 1769--1797, (2016).
PDF
[19] M. Lewicka, P. Ochoa and M.R. Pakzad, Variational models for prestrained plates with Monge- constraint,
Diff. Integral Equations, Vol. 28,861--898, no 9-10 (2015).
PDF
[18] M. Lewicka, L. Mahadevan and M.R. Pakzad, Models for elastic shells with incompatible strains,
Proceedings of the Royal Society A, 470, 1471--2946, (2014).
PDF
[17] Z. Liu and M.R. Pakzad, Rigidity and regularity of co-dimension one Sobolev isometric immersions,
Ann. Sc. Norm. Sup. Pisa - Classe di Scienze. Vol. XIV, issue 3, 76--817, (2015).
PDF
[16] P. Hornung, M. Lewicka and M.R. Pakzad,
Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells,
Journal of Elasticity, Volume 111, Number 1, 1--19, (2013).
PDF
[15] M. Lewicka , L. Mahadevan and M.R. Pakzad,
The Foppl-von Karman equations for plates with incompatible strains,
Proceedings of the Royal Society A 467, 402--426, (2011).
PDF
[14] M. Lewicka and M.R. Pakzad, Scaling laws for non-Euclidean plates and the $W^{2,2}$ isometric
immersions of Riemannian metrics,
ESAIM: Control, Optimisation and Calculus of Variations, Vol. 17, no 4 (2011).
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[13] M. Lewicka and M.R. Pakzad, The infinite hierarchy of elastic shell models:
some recent results and a conjecture,
Infinite Dimensional Dynamical Systems, Fields Institute Communcations 46, pp 407--420, (2013).
PDF
[12] M.R. Pakzad, A note on regularity and rigidity of co-dimension 1 Sobolev isometric immersions,
Preprint (2009). See [17] for the development of the ideas therein.
PDF
[11] M. Lewicka, M.G. Mora and M.R. Pakzad, The matching property of infinitesimal isometries
on elliptic surfaces and elasticity of thin shells,
Arch. Rational Mech. Anal. (3) Vol. 200, 1023--1050, (2011).
PDF
[10] M. Lewicka, M.G. Mora and M.R. Pakzad, A nonlinear theory for shells with slowly varying
thickness,
C.R. Acad. Sci. Paris, Ser I 347, 211--216 (2009).
PDF
[9] M. Lewicka, M.G. Mora and M.R. Pakzad, Shell theories arising as low energy
$\Gamma$-limit of 3d nonlinear elasticity,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX, 1--43 (2010).
PDF
[8] S. Muller and M.R. Pakzad, Convergence of equilibria of thin elastic plates,
the von Karman case,
Comm. Partial Differential Equations, Vol. 33, Issue 6, 1018 -- 1032, (2008).
PDF
[7] S. Muller and M.R. Pakzad, Regularity properties of isometric immersions,
Math. Zeit.
251, no. 2, 313 -- 331, (2005).
PDF
[6] M.R. Pakzad, On the Sobolev space of isometric immersions,
Journal of Differential Geometry, Vol.66, 47 -- 69, (2004).
PDF
[5] M.R. Pakzad, Weak density of smooth maps in
$W^{1,1}(M , N)$ for non-abelian $\pi_1(N)$,
Annals of Global Analysis and Geometry,
23, no. 1, 1 -- 12, (2003).
PDF
[4] M.R. Pakzad and T. Riviere, Weak density of smooth maps for the
Dirichlet energy between Manifolds,
Geometric And Functional Analysis, 13,
no. 1, 223 -- 257, (2003).
PDF
[3] M.R. Pakzad, On topological singular set of maps with finite 3-energy into $\mathbb S^3$,
Zeitschrift fur Analysis und ihre Anwendungen, Journal of Analysis and its Appli-
cations, Vol.21, No.3, 561--568, (2002).
PDF
[2] M.R. Pakzad, Relaxing the Dirichlet energy for maps
into $\mathbb S^2$ in high dimensions,
Communications in Contemporary Mathematics,
Vol.4, No.3, 513 -- 528, (2002).
PDF
[1] M.R. Pakzad, Existence of infinitely many weakly
harmonic maps from a domain in $\mathbb R^n$ into $\mathbb S^2$ for non-constant boundary data,
Calculus of
Variations and Partial Differential Equations, 237, 97 -- 121, (2001).
PDF
Ph.D Thesis
Advisor: Tristan Rivière
ENS de Cachan (now ENS Paris-Saclay), December 2000
Étude des singularités topologiques dans les espaces fonctionnels entre les variétés et applications au calcul des variations
The introduction in English