Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How do I show that the asymptotic speed of the eigenvalues $\lambda$ of the Laplacian Operator is $O(m^{2/n})$ where $m$ is the index of the eigenvalues and $n$ is the dimension of the space?

share|cite|improve this question

1 Answer 1

up vote 3 down vote accepted

This is not a perfect answer, but in the book by J. Roe, "Elliptic operators, topology, and asymptotic methods" there is at the start of chapter 8 a rough estimate along the direction you want. Maybe by using fractional Sobolev exponent and some more thinking it can give what you are after. In the same book later there is a full proof of Weyl's asymptotic formula (which is a stronger statement than what you are after).

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.