Abstract: | The following regularity of weak solutions of a class of elliptic equations of the form are investigated,
|
(*) |
. Here Ω⊂R
n
is a bounded domain, A(x,z,p)=(A1(x,z,p), A2(x,z,p),...,An(x,z,p)) and B(x,z,p) satisfy and for all (x,z,p), (y,m,p)∈Ω×R×R
n
and all ξ∈R
n
, where m≥0, κ≥0, Λ>0 and ϕ(r) is a bounded increasing function in 0, ∞).
The results of the paper are: a) if lim
r→0+ϕ(r)=ϕ(0)=0, then any bounded solution of (*) belongs to C
loc
β
(Ω) for any β∈(0, 1); b) if m=0, and ϕ(r) is Dini continuous, that is, lim
r→0+ϕ(r)=ϕ(0)=0,
, then any bounded solution of (*)∈C
loc
l
(Ω).
Supported by the National Science Foundation of China (19771072) and the Science Foundation of Zhejiang Province (197010). |