Answering a question raised by Y.X. Huang, we prove what follows: if O is a bounded smooth domain and p > 1, then the mapping q → λq |O|^(p/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)(O) into L^q(O)
On a problem of Huang concerning best constants in Sobolev embeddings
IANNIZZOTTO, ANTONIO
2015-01-01
Abstract
Answering a question raised by Y.X. Huang, we prove what follows: if O is a bounded smooth domain and p > 1, then the mapping q → λq |O|^(p/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)(O) into L^q(O)
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