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1. Das Verhalten der Ableitungen globaler L�sungen nichtlinearer Wellengleichungen f�r grosse Zeiten

Author

Hartmut Pecher

Subjects
Pure mathematics, General Mathematics, media_common.quotation_subject, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Algebraic geometry, Type (model theory), Infinity, 01 natural sciences, Infimum and supremum, Nonlinear system, Number theory, Homogeneous, 0103 physical sciences, 010307 mathematical physics, 0101 mathematics, Mathematics, media_common
Abstract

This note deals with the behavior of global classical solutions of a certain type of nonlinear wave-equations when t goes to infinity. Starting with results of Morawetz-Strauss [2] and of the author [3] about the time-decay rates for the spatial supremum of the soluion we estimate all its Sobolev-norms. Our main tools are estimates of the LP-decay rates for homogeneous wave-equations contained in a paper of von Wahl [5].

Published
1974

2. Die monodromie der isolierten singularit�ten von hyperfl�chen

Author

Egbert Brieskorn

Subjects
Pure mathematics, General Mathematics, 010102 general mathematics, Monodromy theorem, Isolated singularity, 01 natural sciences, Cohomology, Algebra, Mathematics::Algebraic Geometry, Monodromy, 0103 physical sciences, Algebraic function, 010307 mathematical physics, 0101 mathematics, Differential algebraic geometry, Mathematics::Symplectic Geometry, Branch point, Mathematics, Singular point of an algebraic variety
Abstract

J. Milnor recently introduced the local Picard-Lefschetz-monodromy of an isolated singularity of a hypersurface. This is an important tool in the investigation of the topology of singularities. The monodromy is an action on a certain cohomology group and is defined in topological terms. In this paper we find an algebraic description of the monodromy. We construct by algebraic methods a regular singular ordinary linear differential operator, such that the monodromy of this singular operator coincides with the Picard-Lefschetz monodromy. As an application we prove that the eigenvalues of the monodromy are roots of unity. Our treatment is close in spirit to Grothendiecks theory of the Gauβ-Manin-connection.

Published
1970