# Regularity of a a transmission problem

How to prove?

Let $a_{ij} \in C^{0, \alpha}(B_1 \cap \mathbb{R}^{n}_{+}), b_{ij} \in C^{0,\alpha}(B_1 \cap \mathbb{R}^{n}_{-})$ elliptic matrices and $$A_{ij}(x) = a_{ij}(x)\chi_{\{ x_n \ge 0 \}} + b_{ij}(x) \chi_{\{x_n \le 0\}}.$$ Show that if $$\mathbb{div}(A_{ij }(x)\nabla u) = 0 \quad \mbox{in} \quad B_1$$ then $u \in \mathrm{Lip}(B_{1/2})$.

Thank you.

-
If you wonder why your question received no answer since April 26... it may be because you did not ask any question here. "To get better answers, you may need to put additional effort into your question... Document your own continued efforts to answer your question." -- from the faq. –  user31373 Aug 3 '12 at 17:30
Oh, now there is an edit adding "How to prove?" at the beginning and "Thank you" at the end. Nope, not any better than it was. Voting to close. –  baba ji Aug 12 at 19:44