@article{CoriascoSchulze2006,
  author    = {Coriasco, Sandro and Schulze, Bert-Wolfgang},
  title     = {Edge problems on configurations with model cones of different dimensions},
  issn      = {0030-6126},
  year      = {2006},
  abstract  = {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},
  language  = {en}
}
@unpublished{CoriascoSchulze2002,
  author    = {Coriasco, Sandro and Schulze, Bert-Wolfgang},
  title     = {Edge problems on configurations with model cones of different dimensions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26438},
  year      = {2002},
  abstract  = {Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj 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 W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.},
  language  = {en}
}
@unpublished{CoriascoSchroheSeiler2001,
  author    = {Coriasco, Sandro and Schrohe, Elmar and Seiler, J{\"o}rg},
  title     = {Bounded imaginary powers of differential operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25962},
  year      = {2001},
  abstract  = {We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B,1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers A up(z), z ∈ C. We also obtain sufficient information on the resolvent of A to show the boundedness of the pure imaginary powers. Examples concern unique solvability and maximal regularity of the solution of the Cauchy problem u' - Δu = f, u(0) = 0, for the Laplacian on conical manifolds.},
  language  = {en}
}
@unpublished{CoriascoPanarese2000,
  author    = {Coriasco, Sandro and Panarese, Paolo},
  title     = {Fourier integral operators defined by classical symbols with exit behaviour},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25896},
  year      = {2000},
  abstract  = {We continue the investigation of the calculus of Fourier Integral Operators (FIOs) in the class of symbols with exit behaviour (SG symbols). Here we analyse what happens when one restricts the choice of amplitude and phase functions to the subclass of the classical SG symbols. It turns out that the main composition theorem, obtained in the environment of general SG classes, has a "classical" counterpart. As an application, we study the Cauchy problem for classical hyperbolic operators of order (1, 1); for such operators we refine the known results about the analogous problem for general SG hyperbolic operators. The material contained here will be used in a forthcoming paper to obtain a Weyl formula for a class of operators defined on manifolds with cylindrical ends, improving the results obtained in [9].},
  language  = {en}
}