7 papers
Flexibility of the isometric immersion system in arbitrary dimension and codimension and the energy scaling of prestrained thin films
Marta Lewicka, Hui Li
We prove that, for a given -regular Riemann metric posed on a -dimensional domain, every short immersion into the Euclidean space , can be uniformly a…
Full flexibility of the Monge-Ampère system in codimension
Wentao Cao, Jonas Hirsch, Dominik Inauen +1
We prove that solutions to the Monge-Ampère system in dimension and codimension , where denotes the Janet dimension, are dense in the spac…
Full flexibility of isometric immersions of metrics with low Hölder regularity in Poznyak theorem's dimension
Marta Lewicka
A classical result by Poznyak asserts that any smooth -dimensional Riemannian metric , posed on the closure of a simply connected domain , has a smooth…
The Monge-Ampère system in dimension two is fully flexible in codimension two
Dominik Inauen, Marta Lewicka
We prove that every -regular subsolution of the Monge-Ampère system posed on a -dimensional domain and with target codimension , can be uniformly ap…
The Monge-Ampere system in dimension two and codimension three
Dominik Inauen, Marta Lewicka
We revisit the convex integration constructions for the Monge-Ampère system and prove its flexibility in dimension and codimension , up to …
The Monge-Ampere system in dimension two: a further regularity improvement
Marta Lewicka
We prove a convex integration result for the Monge-Ampère system, in case of dimension and arbitrary codimension . Our prior result stated flexibility up to the Höld…
Visualization of the convex integration solutions to the Monge-Ampère equation
Luca Codenotti, Marta Lewicka
In this article, we implement the algorithm based on the convex integration result proved in [Lewicka-Pakzad Analysis and PDE (2017)] and obtain visualizations of the first iterati…