Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898941 | Journal of Differential Equations | 2018 | 13 Pages |
Abstract
The Cr dependence problem of multiple Dirichlet eigenvalues on domains is discussed for elliptic operators by regarding Cr+1-smooth one-parameter families of C1 perturbations of domains in Rn. As applications of our main theorem (Theorem 1), we provide a fairly complete description for all eigenvalues of the Laplace operator on disks and squares in R2 and also for its second eigenvalue on balls in Rn for any nâ¥3. The central tool used in our proof is a degenerate implicit function theorem on Banach spaces (Theorem 2) of independent interest.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Julian Haddad, Marcos Montenegro,