| Autor: |
Biagi S., Dipierro S., Valdinoci E., Vecchi E. |
| Přispěvatelé: |
Biagi S., Dipierro S., Valdinoci E., Vecchi E. |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Popis: |
Given a bounded open set $ \Omega\subseteq{\mathbb{R}}^n $, we consider the eigenvalue problem for a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of $ \Omega $. We prove that the second eigenvalue $ \lambda_2(\Omega) $ is always strictly larger than the first eigenvalue $ \lambda_1(B) $ of a ball $ B $ with volume half of that of $ \Omega $. This bound is proven to be sharp, by comparing to the limit case in which $ \Omega $ consists of two equal balls far from each other. More precisely, differently from the local case, an optimal shape for the second eigenvalue problem does not exist, but a minimizing sequence is given by the union of two disjoint balls of half volume whose mutual distance tends to infinity. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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