Polyharmonic Dirichlet Problems: Positivity, Critical Exponents and Critical Dimensions
نویسنده
چکیده
In this summary we want to present the main results which are contained in the author’s “Habilitationsschrift” (dissertation). It has been written in German and has been submitted to the Faculty of Mathematics and Physics of the University of Bayreuth. Moreover we want to comment on these results, sketch some of the ideas how to prove them and give some background information. For the reader’s convenience we keep the numbering of the lemmas (Hilfssatz), theorems (Satz), corollaries (Folgerung), definitions (Definition) and equations of the German original version. Further we refer to its bibliography (Literaturverzeichnis). Some of the results have been obtained in collaboration with Guido Sweers of Delft (in particular Theorems 1.1 and 1.26) and with Francisco Bernis of Madrid (Part b of Theorem 3.2). Parts of this dissertation are based on the papers [BerG], [Gr2], [Gr3], [GS1], [GS2], [GS3]. I am grateful to my colleagues Dr. R. Kaiser, Dr. B. Schmitt and Prof. M. Wiegner for numerous interesting and stimulating discussions. I owe a special gratitude to my academic teacher Prof. W. von Wahl for his permanent support.
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