Henrik Ibsen is known as a major writer of problem plays.
Therefore, statement A is correct.
Ibsen was a Norwegian playwright.
Therefore, statement C is correct.
His famous play A Doll's House was published in \(1879\).
Therefore, statement E is correct.
Statement B is incorrect because Huckleberry Finn was written by Mark Twain, not Ibsen.
Statement D is also incorrect because Young Man Luther was written by John Osborne.
Thus, the correct statements are:
\[
A,\ C,\ E.
\]