Answering a question raised by Y.X. Huang, we prove what follows: if is a p bounded smooth domain and p > 1, then the mapping q → λq || q is decreasing in ]0, p∗[ and Lipschitz continuous on compact subsets of ]0, p∗[, λq being the p-th power of the best Sobolev constant for the embedding of W 1, p () into L q ().
On a problem of Huang concerning best constants in Sobolev embeddings
FARACI, FRANCESCA;
2015-01-01
Abstract
Answering a question raised by Y.X. Huang, we prove what follows: if is a p bounded smooth domain and p > 1, then the mapping q → λq || q is decreasing in ]0, p∗[ and Lipschitz continuous on compact subsets of ]0, p∗[, λq being the p-th power of the best Sobolev constant for the embedding of W 1, p () into L q ().File in questo prodotto:
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