Results 21 to 30 of about 2,989,822 (277)
Boundary Integral Operator for the Fractional Laplace Equation in a Bounded Lipschitz Domain [PDF]
, 2011 We study the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value problem of a fractional Laplace equation.
Tongkeun Chang
semanticscholar +1 more source
Uniform Convergence Rates for Lipschitz Learning on Graphs [PDF]
arXiv.org, 2021 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.
Leon Bungert, J. Calder, Tim Roith
semanticscholar +1 more source
Extending the Applicability of Two-Step Solvers for Solving Equations
Mathematics, 2019 We present a local convergence of two-step solvers for solving nonlinear operator equations under the generalized Lipschitz conditions for the first- and second-order derivatives and for the first order divided differences.
Ioannis K. Argyros, Stepan Shakhno
doaj +1 more source
LipBaB: Computing exact Lipschitz constant of ReLU networks [PDF]
International Conference on Artificial Neural Networks, 2021 The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers.
Aritra Bhowmick +2 more
semanticscholar +1 more source
Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem [PDF]
, 2010 For a domain bounded by homogeneous subsets of a Lipschitz graph, we show the Corona Theorem is affirmative.Comment: 5 ...
NewDelman, Brady Max
core +5 more sources
Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications
Analysis and Geometry in Metric Spaces, 2016 Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1].
Chen Xiaming, Jiang Renjin, Yang Dachun
doaj +1 more source
Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
Journal of Inequalities and Applications, 2017 This paper is concerned with an explicit value of the embedding constant from W 1 , q ( Ω ) $W^{1,q}(\Omega)$ to L p ( Ω ) $L^{p}(\Omega)$ for a domain Ω ⊂ R N $\Omega\subset\mathbb{R}^{N}$ ( N ∈ N $N\in\mathbb{N}$ ), where 1 ≤ q ≤ p ≤ ∞ $1\leq q\leq p ...
Makoto Mizuguchi +3 more
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The mixed problem in L^p for some two-dimensional Lipschitz domains [PDF]
, 2005 We consider the mixed problem for the Laplace operator in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. The boundary of the domain is decomposed into two disjoint sets D and N.
A. Azzam +28 more
core +6 more sources
, 2016 Having a given weight ρ(x) = τ (dist(x,∂Ω)) defined on Lipschitz boundary domain Ω and an Orlicz function Ψ , we construct the subordinated weight ω(·, ·) defined on ∂Ω×∂Ω and extension operator ExtL : Lip(∂Ω) → Lip(Ω) form Lipschitz functions defined on
A. Kałamajska, R. Dhara
semanticscholar +1 more source
Graphs with prescribed the trace of the Levi form [PDF]
, 2005 We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain.
Martino, Vittorio, Montanari, Annamaria
core +1 more source