ﻻ يوجد ملخص باللغة العربية
In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.
In this note we prove in the nonlinear setting of $CD(K,infty)$ spaces the stability of the Krasnoselskii spectrum of the Laplace operator $-Delta$ under measured Gromov-Hausdorff convergence, under an additional compactness assumption satisfied, for
For a given domain $Omega subset Bbb{R}^n$, we consider the variational problem of minimizing the $L^1$-norm of the gradient on $Omega$ of a function $u$ with prescribed continuous boundary values and satisfying a continuous lower obstacle condition
For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely determined b
We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as stochastic
We prove that the energy dissipation property of gradient flows extends to the semigroup maximal operators in various settings. In particular, we show that the vertical maximal function relative to the $p$-parabolic extension does not increase the $d