Volume 3,
Issue 2, 2002
Article
25
STRONGLY ELLIPTIC OPERATORS FOR A PLANE WAVE DIFFRACTION PROBLEM IN BESSEL POTENTIAL SPACES
L.P. CASTRO
DEPARTMENT OF MATHEMATICS,
UNIVERSITY OF AVEIRO,
3810 - 193 AVEIRO,
PORTUGAL
E-Mail: lcastro@mat.ua.pt
Received 08 January, 2001; Accepted 23 January, 2002.
Communicated by: S.S. Dragomir
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ABSTRACT.
We consider a plane wave diffraction problem by a union of several
infinite strips. The problem is formulated as a boundary-transmission one for the Helmholtz equation in a Bessel
potential space setting and where Neumann conditions are assumed
on the strips. Using arguments of strong ellipticity and different
kinds of operator relations between convolution type operators,
it is shown the well-posedness of the problem in a smoothness
neighborhood of the Bessel potential space with finite energy norm.
Key words:
Diffraction
problem, Strong
Ellipticity, Convolution type
operator, Wiener-Hopf
operator, Equivalence after extension.
2000 Mathematics Subject
Classification:
78A45, 35J25,
47B35, 47A50,
47A20, 47A68.
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Other issues
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Volume 1, Issue 1, 2000
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2, 2000
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Volume 2, Issue
1, 2001
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2, 2001
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Volume 2, Issue
3, 2001
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Volume 3, Issue
1, 2002
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Volume 3, Issue
2, 2002
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Volume 3, Issue
3, 2002
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4, 2002
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5, 2002
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Volume 4, Issue
1, 2003
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5, 2003
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