Related papers: Smoothed Projections over Weakly Lipschitz Domains
We study the behavior of the Gorenstein weak global dimension under a cleft extension of rings; we prove that under some mild conditons the finiteness of the Gorenstein weak global dimension is invariant. Moreover, we compare the relative…
We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces as usual, but with different basis functions, so that the…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…
We obtain (weighted) restricted type estimates for the Bergman projection operator on monomial polyhedra, a class of domains generalizing the Hartogs triangle. From these estimates, we recapture $L^p$ boundedness results of the Bergman…
We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in…
In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the…
The construction of $C^m$ conforming finite elements on simplicial meshes has recently advanced through the groundbreaking work of Hu, Lin, and Wu (Found. Comput. Math. 24, 2024). Their framework characterizes smoothness via moments of…
We determine an explicit presentation by generators and relations of the cohomology algebra $H^*(\mathbb P^2\setminus C,\mathbb C)$ of the complement to an algebraic curve $C$ in the complex projective plane $\mathbb P^2$, via the study of…
In this paper, we establish a theorem on extension of Lipschitz maps $f$ definable in Hensel minimal fields $K$. This may be regarded as a definable, non-Archimedean, non-locally compact version of Kirszbraun's extension theorem. We proceed…
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…
We consider Riemann mappings from bounded Lipschitz domains in the plane to a triangle. We show that in this case the Riemann mapping has a linear variational principle: it is the minimizer of the Dirichlet energy over an appropriate affine…
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…
We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic…
We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also…
In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational…
The classical McShane-Whitney extension theorem for Lipschitz functions is refined by showing that for a closed subset of the domain, it remains valid for any interval of the real line. This result is also extended to the setting of locally…
We set up a descriptive set-theoretic framework to study Lipschitz-free spaces and use the reduction argument of Bossard to prove several results. We prove two universality results: if a separable Banach space is isomorphically universal…
We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of $\bar{z}$ to the Bergman space of the…