の上では【のうえでは】

の上では follows a noun and limits a statement to it: "on paper", "according to", "in terms of". The noun is a record, a rule or a model – the law, the data, a map, a theory – and は signals that reality may be different.

The second half often says so outright, with が or けど and じっさい実際は. When it doesn't, the doubt is still there.

Without は, の上で is a plain "in terms of", with no hint that reality differs: しごと仕事のうえ上でのなやみ悩み, "worries to do with work". It is a different thing from the verb pattern たうえ上で, "after doing".

の上では or 上は

A shorter written form puts 上 straight after the noun, read じょう: ほうりつじょう法律上, りろん理論じょう上, けいさんじょう計算上. It means the same, and it keeps the contrast when は follows. You'll find it in formal writing, reports and the news.