Edge problems on configurations with model cones of different dimensions
- Elliptic equations on configurations W = W-1 boolean OR (. . .) boolean OR W-N with edge Y and components W-j of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here edges. Starting from edge-degenerate operators on Wj, j = 1, . . . , N, we construct an algebra with extra 'transmission' conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator- valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on WY. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics
Author details: | Sandro Coriasco, Bert-Wolfgang SchulzeGND |
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URL: | http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.ojm |
ISSN: | 0030-6126 |
Publication type: | Article |
Language: | English |
Year of first publication: | 2006 |
Publication year: | 2006 |
Release date: | 2017/03/24 |
Source: | Osaka journal of mathematics. - ISSN 0030-6126. - 43 (2006), 1, S. 63 - 102 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access |