一类线性椭圆PDE的解的局部有界性

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问题如图，若是点不开图片可以如下


Suppose a_ij∈ L^∞ (B_1 ) and c∈L^(n/2) satisfy following assumptions
a_ij ξ_i ξ_j≥λ|ξ|^2,for any x∈B_1,ξ∈R^n,
and
|a_ij |_(L^∞ )+〖∥c∥〗_(L^q )≤Λ
for some positive constant λ and Λ.  Suppose that u∈H^1 (B_1 ) is a subsolution in the
∫_(B_1)▒〖a_ij D_i uD_j φ+cuφ〗  ≤ ∫_(B_1)▒fφ,
For any φ∈H_0^1 (B_1) andφ≥0 in B_1.
If f∈L^q (B_1 ),for q>n/2
Question : u^+∈L_loc^∞ (B_1) ?

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若答案是否，请问反例该如何构造？