Extension domainsSobolev functionsBV functionsBoundary volumeIn this note, we prove that the boundary of a(W1,p,BV)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\use...
and using Schauder’s estimates and Sobolev’s embedding, we have $$\begin{aligned} \left\Vert v(t_1)-v(t_2)\right\Vert _{C^{2,\sigma _*}(\overline{\Omega })}&\le c_{29}\left\Vert v(t_2)(\hat{u}(t_1)-\hat{u}(t_2))\right\Vert _{C^{\sigma _*}(\overline{\Om...
Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.Analysis.Hofer Mathlib.Analysis.InnerProductSpace.Adjoint Mathlib.Analysis.InnerProductSpace.Basic Mathlib.Analysis.InnerProductSpace.Calculus Mathlib.Analysis.InnerProductSpace.Completion Mathlib.Analysis.InnerProductSpace.ConformalLinearMap Mathlib....
When constructing frames, we do not use the principle of unitary extension. We also consider the approximate properties of the resulting frames for functions from the Sobolev space with logarithmic weight.doi:10.1080/01630563.2023.2228392Taylor And FrancisNumerical Functional Analysis and Optimization...
Cauchy-Riemann's equation $ \\bar{\\partial}u = f $ on $ \\mathbb C $, this article demonstrates a corona-type principle which exists as a somewhat unexpected extension of the analytic Hilbert's Nullstellensatz on $ \\mathbb C $ to the quadratic Fock-Sobolev spaces on $ \\mathbb C ...
3. Here, we need to adapt techniques developed for spectral gap and logarith- mic Sobolev inequalities to the more delicate entropy dissipation estimate. In particular, the one-vertex bound is shown to produce certain covariance terms in Sect. 3.1. The crucial bound on these covariances is ...
Theorem 1.1 Letbe a Lipschitz domain, and letA(x) be a uniformly elliptic symmetric matrix with Lipschitz coefficients defined on. LetBbe a ball centered inand suppose thatis a Lipschitz graph with slope, whereis some positive constant depending only ondand the ellipticity ofA(x). Letbe a sol...