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Theorems about order reduction and localization of such operators in Bessel potential\n                    <jats:italic>H<\/jats:italic>\n                    and H\u00f6lder\u2010Zygmund Z(IR\n                    <jats:sub>n<\/jats:sub>\n                    ) spaces are proved. A pseudodifferential operator\n                    <jats:italic>A<\/jats:italic>\n                    with locally sectorial matrix symbol is proved to be Fredholm in the space\n                    <jats:italic>H<\/jats:italic>\n                    (\n                    <jats:italic>M<\/jats:italic>\n                    ) and Ind A = 0 where s depends on\n                    <jats:italic>A.<\/jats:italic>\n                    Application to a boundary value problem for an elastic body with crack is discussed in conclusion.\n                  <\/jats:p>","DOI":"10.1002\/mana.3211600107","type":"journal-article","created":{"date-parts":[[2010,7,12]],"date-time":"2010-07-12T04:23:04Z","timestamp":1278908584000},"page":"149-191","source":"Crossref","is-referenced-by-count":31,"title":["Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary"],"prefix":"10.1002","volume":"160","author":[{"given":"R.","family":"Duduchava","sequence":"first","affiliation":[]},{"given":"F.\u2010O.","family":"Speck","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,2,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.5802\/aif.116"},{"key":"e_1_2_1_3_2","first-page":"33","volume-title":"Lebesgue spaces of differentiable functions and distributions","author":"Calderon A.","year":"1961"},{"key":"e_1_2_1_4_2","volume-title":"Integral Equation Methods in Scattering Theory","author":"Colton D.","year":"1983"},{"key":"e_1_2_1_5_2","series-title":"vol. 756 of Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0069813","volume-title":"Elliptic Pseudodifferential Operators \u2010 an Abstract Theory","author":"Cordes H.","year":"1979"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0519043"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201149"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500027773"},{"key":"e_1_2_1_9_2","first-page":"19","volume-title":"Proceedings of Symposium on Continuum Mechanics and Related Problems of Analysis","author":"Duduchava R.","year":"1973"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1070\/IM1976v010n02ABEH001699"},{"key":"e_1_2_1_11_2","unstructured":"Duduchava R.: Integral equations with fixed singularities. 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