Zobrazeno 1 - 10
of 1 653
pro vyhledávání: '"49Q20"'
Autor:
Krämer, Fabius, Laux, Tim
We propose and study a novel efficient algorithm for clustering and classification tasks based on the famous MBO scheme. On the one hand, inspired by Jacobs et al. [J. Comp. Phys. 2018], we introduce constraints on the size of clusters leading to a l
Externí odkaz:
http://arxiv.org/abs/2412.17694
Autor:
Barroso, Ana Cristina, Zappale, Elvira
A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the second gradient, as well as a perimet
Externí odkaz:
http://arxiv.org/abs/2412.16027
We give a sufficient condition for H\"older continuity at a boundary point for quasiminima of double-phase functionals of $p,q$-Laplace type, in the setting of metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequal
Externí odkaz:
http://arxiv.org/abs/2412.04978
We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaini
Externí odkaz:
http://arxiv.org/abs/2412.04574
Autor:
Backus, Aidan
Let $M$ be a closed oriented Riemannian manifold of dimension $d$, and let $\rho \in H^{d - 1}(M, \mathbb R)$ have unit norm. We construct a lamination $\lambda_\rho$ whose leaves are exactly the minimal hypersurfaces which are calibrated by every ca
Externí odkaz:
http://arxiv.org/abs/2412.00255
Autor:
Caniato, Riccardo, Rivière, Tristan
We prove that stationary Yang$-$Mills fields in dimensions 5 belonging to the variational class of weak connections are smooth away from a closed singular set $S$ of vanishing 1-dimensional Hausdorff measure. Our proof is based on an $\varepsilon$-re
Externí odkaz:
http://arxiv.org/abs/2411.19910
We study the gradient flow of the Allen-Cahn equation with fixed boundary contact angle in Euclidean domains for initial data with bounded energy. Under general assumptions, we establish both interior and boundary convergence properties for the solut
Externí odkaz:
http://arxiv.org/abs/2411.17979
Autor:
Perugini, Matteo
Let $n\geq 1$, and let $\Omega\subset \mathbb{R}^n$ be an open and connected set with finite Lebesgue measure. Among functions of bounded variation in $\Omega$ we introduce the class of \emph{minimally singular} functions. Inspired by the original th
Externí odkaz:
http://arxiv.org/abs/2411.17633
Autor:
Marchese, Andrea, Merlo, Andrea
We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.
Externí odkaz:
http://arxiv.org/abs/2411.15019
Autor:
De Masi, Luigi, Marchese, Andrea
We prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field $f$ coincides with the gradient of a $C^1$ function $g$, outside a set $E$ of arbitrarily small Lebesgue measure. We replace
Externí odkaz:
http://arxiv.org/abs/2411.15012