MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is a C^1-function in a bounded domain $\Omega\subset R^n;$ an element of the Sobolev space $W^{2,\infty}(\Omega)$ ?

share|cite|improve this question
up vote 2 down vote accepted

No. Consider $x^{3/2}$ on $(-1,1)$. It has Holder continuous but not Lipschitz derivative. See Gilbarg-Trudinger Ch. 4 for some related exercises (e.g. a C^1 function with derivative continuous but not Holder continuous for any $\alpha$).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.