w circumflex and y circumflex are not in the widely used ISO 8859-1 ("Latin-1") character set, which may be what you are using for input. They are available in UTF-8 of course. The other circumflexed letters are part of ISO 8859-1 as they occur in major European languages (apparently Welsh doesn't count
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The forum page displays with a header saying it uses UTF-8, so if the database and form inputs accepted UTF-8, it should all work. You need to be using a browser font with those characters available, too - which not all do, as many are ISO 8859-1 only.
Additionally you can't specify special characters by number in the message posting box as it's filtered by the forum software, but inserting these in raw HTML for an ordinary web site will work on any browser that has a suitable font available: Ŵ ŵ Ŷ ŷ
If everybody used UTF-8 we wouldn't have this problem and many others like it.