Mellin analysis of partial differential equations in papers of B. Ziemian

ArticleOriginal scientific text

Title

Authors ¹

Existence and regularity theorems for Fuchsian type differential operators and the theory of second microlocalization are presented.

Mellin transformation, propagation of singularities, singular elliptic operators

J. M. Bony, Second microlocalization and propagation of singularities for semilinear hyperbolic equations, in: Hyperbolic Equations and Related Topics (Kataka/Tokyo, 1984), Academic Press, Boston, 1986, 11-49.
Z. Szmydt and B. Ziemian, Multidimensional Mellin transformation and partial differential operators with regular singularity, Bull. Polish Acad. Sci. Math. 35 (1987), 167-180.
Z. Szmydt and B. Ziemian, Solutions of singular elliptic equations via the Mellin transformation on sets of high order of tangency to the singular lines, ibid. 36 (1988), 521-535.
Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Kluwer, Dordrecht, 1992.
Z. Szmydt and B. Ziemian, Local existence and regularity of solutions of singular elliptic operators on manifolds with corner singularities, J. Differential Equations 83 (1990), 1-25.
B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics, I, ibid. 101 (1993), 28-57.
B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics, II, in: Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., 1992, 555-580.
B. Ziemian and H. Kołakowski, Second microlocalization and the Mellin transformation, Publ. RIMS Kyoto Univ. 26 (1990), 785-801.