Schauder estimates of the uniformly elliptic equation with a inverse-square potential

作者：Li, Zijin^*

来源：Journal of Mathematical Analysis and Applications, 2018, 464(2): 1352-1365.

DOI：10.1016/j.jmaa.2018.04.064

• Inverse-square potential
• Holder continuity
• Schauder estimates

In this paper, we derive Schauder estimates to the solutions of the following uniformly elliptic equation with a inverse-square potential and nonhomogeneous term @@@ -a(ij)(x)partial derivative(ij)u(x) + A/vertical bar x vertical bar(2)u(x) = f(x), in B, @@@ which lead to the existence and sharp regularity results of the classical solutions. More precisely, we prove that u is an element of C'(n+2 ,r) provided integral is an element of C-n,C- r, a(ij) is an element of C'(n, r) and A > A(2 + n + gamma)(d + n + gamma).

• 出版日期2018-8-15
• 单位南京大学