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Singularities in Quasi‐Banach Spaces with Applications to Semilinear Elliptic Equations I
Author(s) -
Runst Thomas
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211800114
Subject(s) - mathematics , banach space , interpolation space , pure mathematics , mathematical analysis , dual (grammatical number) , gravitational singularity , banach manifold , lp space , functional analysis , art , biochemistry , chemistry , literature , gene
The paper deals with the extension of the singularity theory which was elaborated for Banach spaces to quasi‐Banach spaces. For general quasi‐Banach spaces some striking tools fail: not locally convex, the dual space may be trivial,…. Applying the concept of dual rich quasi ‐ Banach spaces and results about Fredholm maps some results of the classical theory can be carried over. As an application we show in the continuation of this part how one can use these results for the investigation of the solution structure of semilinear elliptic boundary value problems in function Rpaces of Besov ‐ Triebel ‐ Lizorkin type.