On the closability of some positive definite symmetric differential forms on \(C_ 0^{\infty}(\Omega)\)
type: Item
instance of: scholarly article
title: On the closability of some positive definite symmetric differential forms on \(C_ 0^{\infty}(\Omega)\)
zbMATH Open document ID: 0572.58006
DOI: 10.1016/0022-1236(85)90005-9
author: B. George
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: Let D be an open subset of \({\mathbb{R}}^ n\), \(n\geq 2\) and \({\mathcal E}^ a \)Dirichlet form in \(L^ 2(D,m)\), where m is the Radon measure on D. For each integer k with \(1\leq k<n\), let \({\mathcal E}_ k\) be a Dirichlet form on some k-dimensional submanifold \(D_ k\) of D. The paper under review is devoted to the study of the closability problem for the forms \({\mathcal E}_{\alpha}\) and their sums in the real Hilbert space \(L^ 2(D;dx)\), where dx is the Lebesgue measure on D. The main results are proved using a simplified version of the imbedding theorem for the weighted Sobolev spaces \(W^ m_ p(D;(\eta (X))^{\alpha})\).
Mathematics Subject Classification ID: 58C99
Mathematics Subject Classification ID: 28C05
zbMATH DE Number: 3913302
zbMATH Keywords: symmetric differential forms
zbMATH Keywords: Radon measure
zbMATH Keywords: Dirichlet form
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: imbedding theorem for the weighted Sobolev spaces
reviewed by: Mircea Puta
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90005-9
OpenAlex ID: W2091248947
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description: scientific article; zbMATH DE number 3913302