Results 41 to 50 of about 3,355,987 (326)

Homogenization of boundary value problems in perforated Lipschitz domains [PDF]

Journal of Differential Equations, 2021
This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients.
Zhongwei Shen
semanticscholar   +1 more source

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, Kazuaki Tanaka, Kouta Sekine, Shin’ichi Oishi   +3 more
doaj   +1 more source

Integral representation of a solution to the Stokes-Darcy problem [PDF]

, 2015
With methods of potential theory we develop a representation of a solution of the coupled Stokes-Darcy model in a Lipschitz domain for boundary data in H-1 ...
Alessandrini, Arbogast, Chavarría-Krauser, Dahlberg, Dindoš, Fabes, Galdi, Hsiao, Jäger, Kenig, Kilty, Kohr, Kohr, Kohr, Landkof, Lanzani, Lanzani, Layton, Lipnikov, Maremonti, Maz'ya, Maz'ya, Medková, Medková, Medková, Medková, Medková, Mitrea, Mitrea, Müller, Netuka, Netuka, Netuka, Nečas, Odquist, Pozrikidis, Quarteroni, Reidinger, Schechter, Steinbach, Steinbach, Steudle, Tartar, Varnhorn   +43 more
core   +3 more sources

On one extension theorem dealing with weighted Orlicz-Slobodetskii space. Analysis on Lipschitz subgraph and Lipschitz domain

, 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

On Quasi-inversions [PDF]

, 2015
Given a bounded domain $D \subset {\mathbb R}^n$ strictly starlike with respect to $0 \in D\,,$ we define a quasi-inversion w.r.t. the boundary $\partial D \,.$ We show that the quasi-inversion is bi-Lipschitz w.r.t.
Kalaj, David, Vuorinen, Matti, Wang, Gendi   +2 more
core   +1 more source

Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$

Comptes Rendus. Mathématique, 2023
We give, first, two new applications related to the range characterization of the range of trace operator in $H^2(\Omega )$. After this, we characterize the range of trace operator in the Sobolev spaces $ W^{3,p}(\Omega )$ when $\Omega $ is a connected ...
Aibèche, Aissa, Amrouche, Cherif, Bahouli, Bassem   +2 more
doaj   +1 more source

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, B.E.J. Dahlberg, B.E.J. Dahlberg, C.E. Kenig, C.E. Kenig, C.E. Kenig, D. Gilbarg, D.C. Chang, D.S. Jerison, D.S. Jerison, E.B. Fabes, E.M. Stein, G. Savaré, G.C. Verchota, G.M. Lieberman, J. Bergh, J. Lagnese, J.O. Strömberg, Loredana Lanzani, Luca Capogna, M.H. Protter, P. Grisvard, R.M. Brown, R.M. Brown, R.R. Coifman, R.R. Coifman, Russell M. Brown, S.R. Bell, Z. Shen   +28 more
core   +6 more sources

On traces of functions in for Lipschitz domains in

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001
Annalisa Buffa, Giuseppe Geymonat
openalex   +3 more sources

Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary

Analysis and Geometry in Metric Spaces, 2022
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations ...
Gibara Ryan, Shanmugalingam Nageswari
doaj   +1 more source