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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 $\overline{\partial}$- Neumann problem in the Sobolev topology is studied. A new $\overline{\partial}$- Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived.

Copyright American Mathematical Society 1996

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Article Info

• ERA Amer. Math. Soc. 01 (1995), pp. 103-107
• Publisher Identifier: S1079-6762(95)03002-2
• 1991 Mathematics Subject Classification. Primary 35J55; Secondary 35S15, 35N15, 58A14, 58G05.
• Key words and phrases. Hodge theory, de Rham complex, "$\overline{\partial}$"-Neumann complex, elliptic estimates, subelliptic estimates, pseudodifferential boundary problems
• Received by the editors July 29, 1995
• Communicated by Robert Lazarsfeld
• Comments

Luigi Fontana

Dipartimento di Matematica
Via Saldini 50
Università di Milano
20133 Milano (Italy)

E-mail address: fontana@vmimat.mat.unimi.it

Steven G. Krantz

Department of Mathematics
Washington University
St. Louis, MO 63130 (U.S.A)

E-mail address: sk@math.wustl.edu

Marco M. Peloso

Dipartimento di Matematica
Politecnico di Torino
10129 Torino (Italy)

E-mail address: peloso@polito.it

Second author supported in part by the National Science Foundation

Third author supported in part by the Consiglio Nazionale delle Ricerche