Mixed Boundary Value Problems for the Helmholtz Equation in a Quadrant |
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Authors: | L P Castro F -O Speck F S Teixeira |
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Institution: | (1) Department of Mathematics, University of Aveiro, 3810–193 Aveiro, Portugal;(2) Department of Mathematics, I.S.T., Technical University of Lisbon, 1049–001 Lisbon, Portugal |
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Abstract: | The main objective is the study of a class of boundary value problems in weak formulation where two boundary conditions are
given on the half-lines bordering the first quadrant that contain impedance data and oblique derivatives. The associated operators
are reduced by matricial coupling relations to certain boundary pseudodifferential operators which can be analyzed in detail.
Results are: Fredholm criteria, explicit construction of generalized inverses in Bessel potential spaces, eventually after
normalization, and regularity results. Particular interest is devoted to the impedance problem and to the oblique derivative
problem, as well. |
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Keywords: | Primary 35J25 Secondary 30E25 47G30 45E10 47A53 47A20 |
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