{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T21:11:16Z","timestamp":1776114676018,"version":"3.50.1"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"6","license":[{"start":{"date-parts":[[2009,2,14]],"date-time":"2009-02-14T00:00:00Z","timestamp":1234569600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>Boundary value problems originated by the diffraction of an electromagnetic (or acoustic) wave by a rectangular wedge with faces of possible different kinds are analyzed in a Sobolev space framework. The boundary value problems satisfy the Helmholtz equation in the interior (Lipschitz) wedge domain, and are also subject to different combinations of boundary conditions on the faces of the wedge. Namely, the following types of boundary conditions will be under study: Dirichlet-Dirichlet, Neumann-Neumann, Neumann-Dirichlet, Impedance-Dirichlet, and Impedance-Neumann. Potential theory (combined with an appropriate use of extension operators) leads to the reduction of the boundary value problems to integral equations of Fredholm type. Thus, the consideration of single and double layer potentials together with certain reflection operators originate pseudo-differential operators which allow the proof of existence and uniqueness results for the boundary value problems initially posed. Furthermore, explicit solutions are given for all the problems under consideration, and regularity results are obtained for these solutions.<\/p>","DOI":"10.1090\/s0002-9939-08-09288-5","type":"journal-article","created":{"date-parts":[[2008,3,6]],"date-time":"2008-03-06T08:54:05Z","timestamp":1204793645000},"page":"2113-2123","source":"Crossref","is-referenced-by-count":19,"special_numbering":"588","title":["Dirichlet-Neumann-impedance boundary value problems arising in rectangular wedge diffraction problems"],"prefix":"10.1090","volume":"136","author":[{"given":"L.","family":"Castro","sequence":"first","affiliation":[]},{"given":"D.","family":"Kapanadze","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,2,14]]},"reference":[{"key":"1","series-title":"Pitman Research Notes in Mathematics Series","isbn-type":"print","volume-title":"Diffraction by wedges","volume":"322","author":"Budaev, Bair","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/058210310X"},{"key":"2","unstructured":"L.P. Castro and D. Kapanadze, Wave diffraction by a strip with first and second kind boundary conditions: the real wave number case, Math. Nachr., to appear, 12 pp."},{"issue":"5","key":"3","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1002\/mma.794","article-title":"On wave diffraction by a half-plane with different face impedances","volume":"30","author":"Castro, L. P.","year":"2007","journal-title":"Math. Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0170-4214","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1515\/GMJ.2006.251","article-title":"The potential method for the reactance wave diffraction problem in a scale of spaces","volume":"13","author":"Castro, Luis P.","year":"2006","journal-title":"Georgian Math. 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Nauk SSSR 121 (1959), 436\u2013439."},{"key":"14","isbn-type":"print","volume-title":"Strongly elliptic systems and boundary integral equations","author":"McLean, William","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0521663326"},{"key":"15","isbn-type":"print","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/BFb0080611","article-title":"Some solved and unsolved canonical problems of diffraction theory","author":"Meister, Erhard","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/3540184791"},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1216\/jiea\/1181075683","article-title":"Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions","volume":"4","author":"Meister, E.","year":"1992","journal-title":"J. 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