In this chapter we collect some preliminary results that we will use throughout the rest of the book, such as Fréechet derivatives, superposition operators and eak and classical solutions of linear elliptic equations and their eigenvalues. Sobolev function spaces are also outlined, although a more complete treatment is postponed until Appendix A.
KeywordsBanach Space Weak Solution Negative Eigenvalue Fredholm Operator Compact Embedding
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