Electron. J. Differential Equations,
Vol. 2019 (2019), No. 48, pp. 122.
Compactness of the canonical solution operator on
Lipschitz qpseudoconvex boundaries
Sayed Saber
Abstract:
Let
be a bounded Lipschitz qpseudoconvex
domain that admit good weight functions. We shall prove that the canonical
solution operator for the
equation is compact on
the boundary of
and is bounded in the Sobolev space
for some values of k. Moreover, we show that
the Bergman projection and the
Neumann operator
are bounded in the Sobolev space
for some values of k.
If
is smooth, we shall give sufficient conditions for compactness
of the
Neumann operator.
Submitted May 8, 2018. Published April 10, 2019.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Lipschitz domain; qpseudoconvex domain.
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Sayed Saber
Mathematics Department
Faculty of Science
BeniSuef University, Egypt
email: sayedkay@yahoo.com

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