AN OPTIMAL LIMITING 2D SOBOLEV INEQUALITY

作者：Biryuk Andrei^*

来源：Proceedings of the American Mathematical Society, 2010, 138(4): 1461-1470.

• Limiting Sobolev embedding theorems
• double logarithmic inequality

The main goal of this paper is to prove an optimal limiting Sobolev inequality in two dimensions for Holder continuous functions. Additionally, from this inequality we derive the double logarithmic inequality
parallel to u parallel to(L)infinity <= parallel to del u parallel to(L)2/root 2 pi alpha root ln(1+6 root 2 pi alpha parallel to u parallel to((C) over dot)alpha/parallel to del u parallel to(L)2 root ln(1+root 2 pi alp

• 出版日期2010-4