Abstract
We study variations of the first nontrivial eigenvalue of the two-dimensional p-Laplace operator, p > 2, generated by measure preserving quasiconformal mappings. The study is based on the geometric theory of composition operators in Sobolev spaces and sharp embedding theorems. Using a sharp version of the reverse Hölder inequality, we obtain a lower estimate for the first nontrivial eigenvalue in the case of Ahlfors type domains.
Original language | English |
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Pages (from-to) | 503-512 |
Number of pages | 10 |
Journal | Journal of Mathematical Sciences |
Volume | 255 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jun 2021 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Applied Mathematics