Marta Lewicka

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20182026

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6 papers · 1 filter

math.AP2026

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 $C^{r, β}$ -regular Riemann metric posed on a $d$ -dimensional domain, every short immersion into the Euclidean space $R^{d + k}$ , can be uniformly a…

math.AP2026

Full flexibility of the Monge-Ampère system in codimension $d_{*} - d + 1$

Wentao Cao, Jonas Hirsch, Dominik Inauen +1

We prove that $C^{1, α}$ solutions to the Monge-Ampère system in dimension $d$ and codimension $k = d_{*} - d + 1$ , where $d_{*}$ denotes the Janet dimension, are dense in the spac…

math.AP2025

The Monge-Ampère system in dimension two is fully flexible in codimension two

Dominik Inauen, Marta Lewicka

We prove that every $C^{1} (ω ˉ)$ -regular subsolution of the Monge-Ampère system posed on a $2$ -dimensional domain $ω$ and with target codimension $2$ , can be uniformly ap…

math.AP2025

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 $d = 2$ and codimension $k = 3$ , up to $C^{1, 1 - 1/ 5}$ …

math.AP2024

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 $d = 2$ and arbitrary codimension $k \geq 1$ . Our prior result stated flexibility up to the Höld…

math.AP2018

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…