SOLUTION TO $\overline{\partial}$ PROBLEM WITH EXACT SUPPORT AND REGULARITY FOR THE $\overline{\partial}$-NEUMANN OPERATOR ON WEAKLY q-CONVEX DOMAINS
2010 ◽
Vol 07
(01)
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pp. 135-142
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Keyword(s):
Let Ω be a weakly q-convex domain in ℂn. We establish the L2 existence theorem for the [Formula: see text]-Neumann operator N when the boundary of Ω is C1. Using this result, we study the [Formula: see text] problem with exact support on such domains. Furthermore, there exists a number ℓ0 > 0 such that the operators N, [Formula: see text] and the Bergman projection are regular in the Sobolev space Wℓ(Ω) for ℓ < ℓ0 when the boundary of Ω is C∞.
Keyword(s):
1973 ◽
Vol 74
(1)
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pp. 107-116
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Keyword(s):
1984 ◽
Vol 37
(1)
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pp. 85-90
2001 ◽
Vol 163
◽
pp. 215-227
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Keyword(s):
2013 ◽
Vol 24
(14)
◽
pp. 1350108
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2003 ◽
Vol 86
(1)
◽
pp. 131-152
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