On a Sobolev-type inequality

  • Angelo Alvino

    Università degli Studi di Napoli Federico II, Italy


A new proof of the classical Sobolev inequality in with the best constant is given. The result follows from an intermediate inequality which connects in a sharp way the norm of the gradient of a function to and -weak norms of , where and is the Sobolev exponent.

Cite this article

Angelo Alvino, On a Sobolev-type inequality. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 4, pp. 379–386

DOI 10.4171/RLM/553