| Autor: |
Brasco, Lorenzo, Lindgren, Erik |
| Předmět: |
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| Zdroj: |
Transactions of the American Mathematical Society; 2023, Vol. 376 Issue 5, p3541-3584, 44p |
| Abstrakt: |
We study the sharp constant for the embedding of W^{1,p}_0(\Omega) into L^q(\Omega), in the case 2p and q is sufficiently close to p, extremal functions attaining the sharp constant are unique, up to a multiplicative constant. This in turn gives the uniqueness of solutions with minimal energy to the Lane-Emden equation, with super-homogeneous right-hand side. The result is achieved by suitably adapting a linearization argument due to C.-S. Lin. We rely on some fine estimates for solutions of p-Laplace–type equations by L. Damascelli and B. Sciunzi. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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