Methods and Applications of Analysis

Volume 15 (2008)

Number 2

A Class of Sobolev Type Inequalities

Pages: 263 – 276

DOI: https://dx.doi.org/10.4310/MAA.2008.v15.n2.a10

Authors

Gu-Ji Tian

Xu-Jia Wang

Abstract

In this paper, we prove that for any strictly convex polynomial, or more generally any strictly convex function satisfying appropriate conditions, there is an associated Sobolev type inequality.

Keywords

Sobolev inequality, Green function, elliptic equation

2010 Mathematics Subject Classification

35J60, 46E35

Published 1 January 2008