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pro vyhledávání: '"Lewicka, Marta"'
Autor:
Lewicka, Marta
We prove a convex integration result for the Monge-Amp\`ere system, in case of dimension $d=2$ and arbitrary codimension $k\geq 1$. Our prior result stated flexibility up to the H\"older regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$, whereas presentl
Externí odkaz:
http://arxiv.org/abs/2405.00231
Autor:
Han, Qing, Lewicka, Marta
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the mathematical physic
Externí odkaz:
http://arxiv.org/abs/2310.02566
Autor:
Lewicka, Marta
We prove a convex integration result for the Monge-Ampere system in dimension $d=2$ and arbitrary codimension $k\geq 1$. We achieve flexibility up to the Holder regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$, improving hence the previous $\mathcal{C}^
Externí odkaz:
http://arxiv.org/abs/2308.13719
Autor:
Lewicka, Marta
In this paper, we study flexibility of the weak solutions to the Monge-Amp\`ere system (MA) via convex integration. This system of Pdes is an extension of the Monge-Amp\`ere equation in $d=2$ dimensions, naturally arising from the prescribed curvatur
Externí odkaz:
http://arxiv.org/abs/2210.04363
The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the geometric m
Externí odkaz:
http://arxiv.org/abs/2112.13699
Autor:
Lewicka, Marta, Mahadevan, L.
The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics and mathemati
Externí odkaz:
http://arxiv.org/abs/2104.08988
Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled and limit
Externí odkaz:
http://arxiv.org/abs/2104.03486
We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the F\"oppl-von K\'arm\'an equations, we
Externí odkaz:
http://arxiv.org/abs/2010.07672
Publikováno v:
Asymptot. Anal., 127(3):201--216, 2022
We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional $\infty$-Laplacian $\Delta_\infty^s$ for $s\in (\frac{1}{2},1)$. This operator has been introduced and first studied in [Bjorland, C., C
Externí odkaz:
http://arxiv.org/abs/2007.15765