The Calder\'on-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds

By Batu Guneysu, S. Pigola. 2014

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We introduce the concept of Calderon-Zygmund inequalities on Riemannian manifolds. For $1 0$. Such an inequality can hold or fail, depending on the underlying Riemannian geometry. After establishing some generally valid facts and consequences of the Calderon-Zygmund inequality (like new denseness results for second order $\mathsf{L}^p$-Sobolev spaces and gradient estimates), we establish sufficient geometric criteria for the validity of these inequalities on possibly noncompact Riemannian manifolds. These results in particular apply to many noncompact hypersurfaces of constant mean curvature.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e996785b4dceb9a488f21ab2265d41bfe7bad1c7