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 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
, accepted in Annales de l'Institut Henri Poincare (C) Non Linear Analysis
(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)
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
L. Codenotti, M. Lewicka and J.J. Manfredi
Discrete approximations to the double-obstacle problem, and
optimal stopping of tug-of-war games , accepted in Transactions
of the AMS (PDF )
M. Lewicka and J.J. Manfredi
The obstacle problem for the p-Laplacian via Tug-of-War games
, accepted in Probability Theory and Related Fields
(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 , submitted
(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
M. Lewicka and R. Pakzad
Prestrained elasticity: from shape formation to Monge-Ampere
anomalies , to appear in the 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)