Calculus of Variations on Thin Prestressed Films. Asymptotic Methods in Elasticity.,
Birkhauser, Progress in Nonlinear Differential Equations and Their
Applications, Vol 101, 460 pp (2023).
(PDF)
M. Lewicka and L. Mahadevan
Geometry, Analysis and Morphogenesis: Problems and Prospects
, Bulletin of the American Mathematical Society 59, 331--369 (2022).
(PDF)
S. Jimenez-Bolanos and M. Lewicka
Dimension reduction for thin films prestrained by shallow
curvature , Proceeding of the Royal Society A, Volume 477, Issue 2247 (2021).
(PDF)
M. Lewicka
Quantitative immersability of Riemann metrics and the infinite
hierarchy of prestrained shell models , Archive for Rational
Mechanics and Analysis 236, 1677--1707 (2020).
(PDF)
M. Lewicka and D. Lucic
Dimension reduction for thin films with transversally varying
prestrian: the oscillatory and the non-oscillatory case ,
Communications on Pure and Applied Mathematics, 73(9), 1880--1932 (2020).
(PDF)
M. Lewicka, A. Raoult and D. Ricciotti
Plates with incompatible prestrain of higher order ,
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 34(7)
(2017), 1883--1912.
(PDF)
A. Acharya, M. Lewicka and R. Pakzad
A note on the metric-restricted inverse design problem ,
Nonlinearity 29 (2016), 1769--1797.
(PDF)
M. Lewicka, P. Ochoa and R. Pakzad
Variational models for prestrained plates with Monge-Ampere
constraint , Diff. Integral Equations, Vol. 28, no 9-10 (2015), 861--898.
(PDF)
On the variational limits of lattice energies on prestrained
elastic bodies , in: ``Differential Geometry and Continuum
Mechanics'' Editors Gui-Qiang G. Chen, Michael Grinfeld and
R.J. Knops, ISBN: 978-3-319-18572-9 (2015), 281--306.
(PDF)
M. Lewicka, L. Mahadevan and M. Pakzad
The Foppl-von Karman equations for plates with incompatible
strains , Proceedings of the Royal Society A 467 (2011),
402--426 (PDF)
M. Lewicka and M. 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), 1158--1173
(PDF)
Papers on Kirigami
G. Chaudhary, L. Niu, M. Lewicka, Q. Han and L. Mahadevan
Geometric mechanics of ordered and disordered kirigami ,
Proceedings of the Royal Society (A). Volume 479, Issue 2274, (2023)
(PDF)
Q. Han, M. Lewicka and L. Mahadevan
Isometric immersions with rectifiable geodesics ,
accepted in: Rocky Mountain Math J. (2023).
(PDF)
Papers on Convex Integration
M. Lewicka
The Monge-Ampere system: convex integration with
improved regularity in dimension two and arbitrary codimension , submitted.
(PDF)
M. Lewicka
The Monge-Ampere system: convex integration in arbitrary
dimension and codimension , submitted.
(PDF)
L. Codenotti and M. Lewicka
Visualization of the convex integration solutions to the
Monge-Ampere equation , AIMS: Evolution Equations and
Control Theory 8(2), 273--300 (2019).
(PDF)
M. Lewicka and R. Pakzad
Convex integration for the Monge-Ampere equation in two
dimensions , Analysis and
PDE, Vol. 10 (2017) (PDF)
Papers on Elasticity of Shells and Dimension Reduction
M. Lewicka, L. Mahadevan and M. Pakzad
The Monge-Ampere 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, (2017), 45--67.
(PDF)
M. Lewicka and H. Li
Convergence of equilibria for incompressible elastic plates
in the von Karman regime , Communications on Pure and
Applied Analysis, Vol 14, Issue 1 (January 2015), doi: 10.3934/cpaa.2014.14.
(PDF)
M. Lewicka, L. Mahadevan and M. Pakzad
Models for elastic shells with incompatible strains
, Proceedings of the Royal Society A, 470 2165 20130604; 1471--2946 (2014)
(PDF)
P. Hornung, M. Lewicka and R. Pakzad
Infinitesimal isometries on developable surfaces and
asymptotic theories for thin developable shells
, Journal of Elasticity, Volume 111, Number 1 (2013)
(PDF)
M. Lewicka and M. Pakzad
The infinite hierarchy of elastic shell models:
some recent results and a conjecture , Infinite Dimensional Dynamical
Systems, Fields Institute Communications 64, 407--420, (2013).
(PDF)
M. Lewicka, M.G. Mora and M. Pakzad
The matching property of infinitesimal isometries on elliptic
surfaces and elasticity of thin shells ,
Arch. Rational Mech. Anal. (3) Vol. 200 (2011), 1023--1050
(PDF)
M. Lewicka
A note on the convergence of low energy critical points of
nonlinear elasticity functionals, for thin shells of arbitrary geometry ,
ESAIM: Control, Optimisation and Calculus of Variations,
17 (2011) 493--505
(PDF)
M. Lewicka, M.G. Mora and M. Pakzad
Shell theories arising as low energy \Gamma-limit of 3d nonlinear elasticity ,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010), 1--43
(PDF)
M. Lewicka, M.G. Mora and M. Pakzad
A nonlinear theory for shells with slowly varying thickness ,
C.R. Acad. Sci. Paris, Ser I 347 (2009), 211--216
(PDF)
A paper on growth
A. Bressan and M. Lewicka
A model of controlled growth , Archive for Rational
Mechanics and Analysis 227(3), 1223--1266 (2018).
(PDF )
Papers on Korn's Inequality
M. Lewicka and S. Muller
On the optimal constants in Korn's and geometric rigidity
estimates in bounded and unbounded domains, under Neumann boundary
conditions , Indiana Univ. Math. J. 65 No. 2 (2016), 377--397.
(PDF)
M. Lewicka and S. Muller
The uniform Korn - Poincare inequality in thin domains
, Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Volume 28, Issue 3, May-June 2011, 443--469
(PDF)
Papers related to Game Theory
F. del Teso, J. Endal and M. Lewicka
On asymptotic expansions for the fractional infinity
Laplacian , Asymptotic Analysis, vol. 127 (3), 201--216 (2022).
(PDF )
M. Lewicka
Non-local Tug-of-War with noise for the geometric fractional
p-Laplacian , Advances in Differential Equations
Volume 27 (1-2) January/February 2022.
(PDF )
J. Calder, N. Garcia Trillos and M. Lewicka
Lipschitz regularity of graph Laplacians on random data
clouds , SIAM J. Math. Anal. vol. 54 (1),
1169--1222, (2022).
(PDF )
M. Lewicka
A Course on Tug-of-War Games with Random Noise. Introduction
and Basic Constructions , Springer Universitext, 254 pp (2020).
(PDF )
M. Lewicka and Y. Peres
The Robin mean value equation II: Asymptotic Holder
regularity , accepted in: Potential Theory (2019).
(PDF )
M. Lewicka and Y. Peres
The Robin mean value equation I: A random walk approach to the
third boundary value problem , accepted in: Potential Theory (2019).
(PDF )
M. Lewicka, J. Manfredi and D. Ricciotti
Random walks and random
tug-of-war in the Heisenberg group , Mathematische Annalen 377, 797–-846 (2020).
(PDF )
M. Lewicka
Random Tug of War games for the p-Laplacian ,
accepted in: Indiana Univ. Math. J. (2019).
(PDF )
M. Lewicka and Y. Peres
Which domains have two-sided supporting unit spheres at every
boundary point? , Expositiones Mathematicae, 38(4), 548--558 (2020).
(PDF )
Discrete approximations to the double-obstacle problem, and
optimal stopping of tug-of-war games ,
Trans. Amer. Math. Soc. 369, 7387--7403 (2017) (PDF )
M. Lewicka and J.J. Manfredi
The obstacle problem for the p-Laplacian via Tug-of-War games
, Probability Theory and Related Fields, Vol 167, Issue 1–2,
349--378 (2017).
(PDF )
Papers related to Fluid Dynamics
P. Bella, E. Feireisl, M. Lewicka and A. Novotny
A rigorous justification of the Euler and Navier-Stokes
equations with geometric effects , SIAM J. Math. Anal., 48(6),
3907--3930 (2017)
(PDF )
M. Lewicka and M. Raoofi
A stability result for the Stokes-Boussinesq equations in infinite 3d channels
, Communications on Pure and Applied
Analysis, Vol 12, Issue 6, 2615--2625 (2013)
(PDF)
M. Lewicka and P.B. Mucha
On the existence of traveling waves in the 3D Boussinesq system ,
Commun. Math. Phys. 292 (2009), 417--429
(PDF)
M. Lewicka
Existence of traveling waves in the Stokes-Boussinesq system for
reactive flow , J. Differential Equations, 237 (2007), no. 2, 343--371
(PDF)
P. Constantin, M. Lewicka and L. Ryzhik
A note on traveling waves
in the 2D Navier-Stokes-Boussinesq system with the no-slip boundary condition ,
Nonlinearity, 19 (2006), 2605--2615
(PDF)
M. Lewicka and P.B. Mucha
On temporal asymptotics for the p'th power viscous reactive gas ,
Nonlinear Anal. 57 (2004), no. 7-8, 951--969
(PDF)
M. Lewicka and S.J. Watson
Temporal asymptotics for the p'th power newtonian fluid in one space dimension ,
Z. Angew. Math. Phys., 54 (2003), no. 4, 633--651.
(PDF)
Papers on Conservation Laws
M. Lewicka and P.B. Mucha
A local and global well-posedness results for the general stress-assisted
diffusion systems , Journal of Elasticity, Vol 123, Issue 1
(2016) 19--41 (PDF )
M. Lewicka and P.B. Mucha
A local existence result for a system of viscoelasticity with physical viscosity
, Evolution Equations and Control Theory, Vol 2, Issue 2,
337--353 (2013)
(PDF)
B. Barker, M. Lewicka and K. Zumbrun
Existence and stability of viscoelastic shock profiles ,
Arch. Rational Mech. Anal. Volume 200, Number 2, (2011) 491--532
(PDF)
M. Lewicka and K. Zumbrun
Spectral stability conditions for shock wave patterns ,
Journal of Hyperbolic Equations, 4 (2007), no. 1, 1--16.
(PDF)
M. Lewicka
Stability conditions for strong rarefaction waves ,
SIAM J. Math. Anal. 36 (2005), no. 4, 1346--1369
(PDF)
M. Lewicka
Lyapunov functional for solutions of
systems of conservation laws containing a strong rarefaction ,
SIAM J. Math. Anal. 36 (2005), no. 5, 1371--1399
(PDF)
M. Lewicka
The well posedness for hyperbolic systems
of conservation laws with large BV data ,
Arch. Rational Mech. Anal. 173 (2004), 415--445
(PDF)
M. Lewicka and K. Trivisa
On the L1 well posedness of systems of conservation laws near solutions containing two
large shocks , J. Differential Equations, 179 (2002), 133--177
(PDF)
M. Lewicka
Stability conditions for patterns of non-interacting large shock waves ,
SIAM J. Math. Anal., 32 no. 5 (2001), 1094--1116
(PDF)
M. Lewicka
L1 stability of patterns of non-interacting
large shock waves , Indiana Univ. Math. J., 49 (2000), 1515--1537
(PDF)
A. Bressan and M. Lewicka
A uniqueness condition for hyperbolic systems of conservation laws ,
Discrete and Continuous Dynamical Systems, 6 no. 3 (2000), 673--682
(PDF)
M. Lewicka
On the well posedness of a system of balance
laws with L\infty data ,
Rend. Sem. Mat. Univ. Padova, 102 (1999), 319--340
(PDF)
A. Bressan and M. Lewicka
Shift differentials of maps in BV Spaces ,
in: 'Nonlinear Theory of Generalized Functions --
Proceedings of the Workshop Nonlinear Theory of Nonlinear Functions,
Vienna 1997', Chapman&Hall
(PDF)
Papers on second order ODEs on manifolds
M. Lewicka and M. Spadini
Branches of forced oscillations in degenerate systems
of second order ODEs , Nonlinear Analysis 68 (2008), 2623--2628
(PDF)
M. Lewicka and M. Spadini
A remark on the genericity of multiplicity results for forced oscillations on manifolds ,
Annali di Mat. Pura ed Applicata, 181 (2002), 85--94
(PDF)
M. Lewicka and M. Spadini
On the genericity of the multiplicity results for forced oscillations on compact manifolds ,
Nonlinear Diff. Equ. Appl., 6 (1999), 357--369.
(PDF)
Other papers
M. Lewicka
Locally lipschitzian guiding function method for ODEs ,
Nonlinear Analysis 33 (1998), 747--758.
(PDF)
J. Andres, L. Gorniewicz and M. Lewicka
Partially dissipative periodic processes ,
Banach Center Publications, Warszawa 1996.
Review papers on various topics
Q. Han and M. Lewicka
Isometric immersions and applications , to appear in
Notices of the AMS (2023).
(PDF)
M. Lewicka and A. Raoult
Thin structures with imposed metric , ESAIM: Proceedings and Surveys
62, 79--90 (2018).
(PDF )
M. Lewicka and R. Pakzad
Prestrained elasticity: from shape formation to Monge-Ampere
anomalies , Notices of the AMS (January 2016)
(PDF )
Here is the original unedited (longer) version of the same paper:
(PDF )
M. Lewicka and J. Manfredi
Game theoretical methods in PDEs , Bollettino dell'Unione
Matematica Italiana: Volume 7, Issue 3 (2014), 211--216
( PDF )
M. Lewicka
Reduced theories in nonlinear elasticity ,
accepted in "Nonlinear Conservation Laws and Applications"
IMA Volume 153 in Mathematics and its Applications, Springer (2011)
393--404
(PDF)
M. Lewicka
Morphogenesis by growth and non-Euclidean elasticity:
scaling laws and thin film models ,
Progress in Nonlinear Differential Equations and Their Applications,
Vol. 60, 433--445, Springer Basel AG
(PDF)
M. Lewicka
On the L1 stability of multi-shock solutions to the Riemann problem ,
International Series of Numerical Mathematics, 141 (2001), 653--662
(PDF)