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ISSN 1079-6762
Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space
Authors:
Luigi Fontana, Steven G. Krantz and Marco M. Peloso
Journal:
Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 103-107
MSC (1991):
Primary 35J55, 35S15, 35N15, 58A14, 58G05
DOI:
https://doi.org/10.1090/S1079-6762-95-03002-2
MathSciNet review:
1369640
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied. As a result, a new elliptic boundary value problem is obtained. Next, the Hodge theory of the $\bar {\partial }$-Neumann problem in the Sobolev topology is studied. A new $\bar {\partial }$-Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived.
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- L. Fontana, S. G. Krantz, M. M. Peloso, Hodge theory in the Sobolev topology for the de Rham complex, preprint.
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Additional Information
Luigi Fontana
Affiliation:
Dipartimento di Matematica Via Saldini 50 Università di Milano 20133 Milano (Italy)
Email:
fontana@vmimat.mat.unimi.it
Steven G. Krantz
Affiliation:
Department of Mathematics Washington University St. Louis, MO 63130 (U.S.A.)
Email:
sk@math.wustl.edu
Marco M. Peloso
Affiliation:
Dipartimento di Matematica Politecnico di Torino 10129 Torino (Italy)
Email:
peloso@polito.it
Keywords:
Hodge theory,
de Rham complex,
$\bar {\partial }$-Neumann complex,
elliptic estimates,
subelliptic estimates,
pseudodifferential boundary problems
Received by editor(s):
July 29, 1995
Additional Notes:
Second author supported in part by the National Science Foundation
Third author supported in part by the Consiglio Nazionale delle Ricerche
Article copyright:
© Copyright 1996
American Mathematical Society