Publications of Marta Lewicka

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Papers on Elasticity with Prestrain

M. Lewicka and R. Pakzad
Convex integration for the Monge-Ampere equation in two dimensions , submitted (PDF )

M. Lewicka, A. Raoult and D. Ricciotti
Plates with incompatible prestrain of higher order , submitted (PDF )

A. Acharya, M. Lewicka and R. Pakzad
A note on the metric-restricted inverse design problem , submitted (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 )

K. Bhattacharya, M. Lewicka and M. Schaffner
Plates with incompatible prestrain , accepted in Arch. Rational Mech. Anal. (PDF )

M. Lewicka and P. Ochoa
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 , accepted in Indiana Math. Univ. Journal (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

M. Lewicka and J.J. Manfredi
The obstacle problem for the p-Laplacian via Tug-of-War games , submitted (PDF )


Papers related to Fluid Dynamics

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 , submitted (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:

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)