Abstract
In this note we consider the solution of the degenerate elliptic system (1) { div ( F ( | x | ) ∇ u ) = 0 , x ∈ B 1 / { 0 } u | ∂ B 1 = ϕ ∈ C ( ∂ B 1 ) where B 1 denotes the unit ball in R n and F is smooth and increasing on [ 0 , 1 ] with F ( 0 ) = 0 , F ( r ) > 0 ( r > 0 ) . It is known that there exists a unique solution u ∈ C ∞ ( B 1 / { 0 } ) ∩ L ∞ ( B 1 ) to this elliptic system. Here we will study the property of u at the origin. At first we give the necessary and sufficient condition such that u can be extended to a continuous function in B . Furthermore, we also give the necessary and sufficient condition such that u is a Hölder continuous function in B 1 .
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