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Some remarks on Riesz transforms on exterior Lipschitz domains

open access: yesForum of Mathematics, Sigma
Let $n\ge 2$ and $\mathcal {L}=-\mathrm {div}(A\nabla \cdot )$ be an elliptic operator on $\mathbb {R}^n$ . Given an exterior Lipschitz domain $\Omega $ , let $\mathcal {L}_D$ be the elliptic operator $\mathcal {L}$
Renjin Jiang, Sibei Yang
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Geometric characterization of generalized Hajłasz-Sobolev embedding domains

open access: yesAdvances in Nonlinear Analysis
In this article, the authors study the embedding properties of Hajłasz-Sobolev spaces with generalized smoothness on Euclidean domains, whose regularity is described via a smoothness weight function ϕ:[0,∞)→[0,∞)\phi :\left[0,\infty )\to \left[0,\infty ).
Li Ziwei, Yang Dachun, Yuan Wen
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