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Start Over Search Limiters Available in Library Collection Topic 0101 mathematics Topic general mathematics Topic mathematics Publication Year Range More than 50 years ago Publisher springer science and business media llc
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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