Some Poincaré--Sobolev inequalities for differential forms

2025/07/08 by Gol'dshtein, Vladimir, Kopylov, Yaroslav, Panenko, Roman
#Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.05851

Abstract

We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Gol'dshtein and Troyanov. As in this paper, our study is based on relations between L_q,p-cohomology and Sobolev type inequalities. The~main results are estimates for the norms of the embedding operators for q=p and p>(n-1)/(k-1) in the~Euclidean r-ball B(r) and its bi-Lipschitz images. We also study the~compactness of such operators.

Citations

• The Lavrentiev phenomenon in calculus of variations with differential forms
• Poincaré duality for L^p cohomology on subanalytic singular spaces

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