The Continuity of Solutions of Elliptic Equations
LIANG Xi-ting (Department of Mathematics, Zhongshan University, Guangzhou 510275,Guangdong, China)
Consider the elliptic equation in integral formwith the aid of Green function the continuity interior to G is proved to the weak solution of the equation under the weaker conditions on f(x), that is, f(x) satisfies (i)andwith w(r) satisfying w(r)→0 as r→0 andor (ii) f(x) satisfiesThe latter condition is equivalent to the Stummel-Kato condition:where η(r) is an increasing founction in (0, diamG) and η(r)→0 as r→0. }. The equationis also considered.
【CateGory Index】： O175.24