A new proof of the classical Sobolev inequality in R^n and its best constant are given. The result follows from an intermediate inequality which connects in a sharp way the L^p norm of the gradient of a function u to its L^p* and L^p*-weak norms; here pє]1,n[ and p*=np/(n-p) is the Sobolev exponent.
On a Sobolev-type inequality / Alvino, Angelo. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1720-0768. - STAMPA. - 20:4(2009), pp. 333-340.
On a Sobolev-type inequality
ALVINO, ANGELO
2009
Abstract
A new proof of the classical Sobolev inequality in R^n and its best constant are given. The result follows from an intermediate inequality which connects in a sharp way the L^p norm of the gradient of a function u to its L^p* and L^p*-weak norms; here pє]1,n[ and p*=np/(n-p) is the Sobolev exponent.File in questo prodotto:
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