Related papers: Relative Lipschitz-like property of parametric sys…
We continue the development of the theory of infinitesimal Lipschitz equivalence, showing the genericity of the condition for families of hypersurfaces with isolated singularities.
Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group. We show that only a quotient of this group remains meaningful in…
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on Relaxed Constant Rank Constraint Qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this aim…
We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains…
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by…
In this article, we study the Lipschitz Geometry at infinity of complex analytic sets and we obtain results on algebraicity of analytic sets and on Bernstein's problem. Moser's Bernstein Theorem says that a minimal hypersurface which is a…
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…
We develop finite element exterior calculus over weakly Lipschitz domains. Specifically, we construct commuting projections from $L^p$ de~Rham complexes over weakly Lipschitz domains onto finite element de~Rham complexes. These projections…
In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the lateral boundary, provided homogeneous Dirichlet data are…
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…
Level proximal subdifferential was introduced by Rockafellar recently for studying proximal mappings of possibly nonconvex functions. In this paper a systematic study of level proximal subdifferential is given. We characterize variational…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
A special type of coarea inequality is proved for compositions of intrinsically Lipschitz mappings of Carnot groups with projections along horizontal vector fields. It is proved that the equality is achieved for mappings with finite…
We investigate the (ambient) bi-Lipschitz V-equivalence of two-variable mixed polynomials satisfying the Newton inner non-degeneracy condition. Concerning triviality, we show that ambient bi-Lipschitz V-triviality for families $\{f +…
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
We present a general framework, treating Lipschitz domains in Riemannian manifolds, that provides conditions guaranteeing the existence of norming sets and generalized local polynomial reproduction - a powerful tool used in the analysis of…
In this article we consider a priori error and pointwise estimates for finite element approximations of solutions to semilinear elliptic boundary value problems in d>=2 space dimensions, with nonlinearities satisfying critical growth…
We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz…