Variable exponent spaces of differential forms on Riemannian manifold
type: Item
instance of: scholarly article
title: Variable exponent spaces of differential forms on Riemannian manifold
zbMATH Open document ID: 1264.46025
DOI: 10.1155/2012/575819
author: Yongqiang Fu
author: Lifeng Guo
published in: Journal of Function Spaces and Applications
publication date: 2012-11-07T00:00:00Z
review text: Summary: We introduce the Lebesgue space and the exterior Sobolev space for differential forms on a Riemannian manifold \(M\), which are the Lebesgue space and the Sobolev space of functions on \(M\), respectively, when the degree of the differential forms is zero. After discussing the properties of these spaces, we obtain the existence and uniqueness of a weak solution for Dirichlet problems of nonhomogeneous \(p(m)\)-harmonic equations with variable growth in \(W^{1,p(m)}_0(\Lambda^k M)\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 58A10
zbMATH DE Number: 6102736
zbMATH Keywords: Lebesgue space
zbMATH Keywords: Sobolev space
zbMATH Keywords: differential forms
zbMATH Keywords: Riemannian manifold
Wikidata QID: Q58908318
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/575819
OpenAlex ID: W2037967642
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description: scientific article; zbMATH DE number 6102736