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 ().
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/41546
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