7
$\begingroup$

I would like to know if anyone has an electronic copy of the following paper:

"Holmgren, E.: Über Systeme von linearen partiellen Differentialgleichungen. Översigt Vetensk. Akad. Handlingar 58, 91–105 (1901)"

In my search, the best result I found was the (possible) statement of the main result of this article which can be found in the following article: https://people.kth.se/~haakanh/publications/Hed-MZ2.pdf. More precisely,

Theorem (Holmgren) Suppose $I$ is a real-analytic nontrivial arc of $\partial \Omega$. Then if $u$ is smooth on a planar neighbohood $\mathcal{O}$ of $I$ and $\Delta^N u=0$ holds on $\mathcal{O} \cap \Omega$ with $\partial_{n}^{j-1}|_I=0$ for $j=1, \dots, 2N$, then $u(z)=0$ on $\mathcal{O} \cap \Omega$, provided that the open set $\mathcal{O} \cap \Omega$ is connected.

Any information is welcome, for example, if this article is published in a book.

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ The article has a zbMath entry, with a short abstract. This article by Hörmander also gives an overview. As a curious coincidence my grandfather Benny Brodda (who studied for some time under Hörmander) gave an extension to this theorem (using a generalisation due to F. John), see this article. I have not been able to find a copy of Holmgren's article yet. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Aug 17, 2021 at 21:23
  • 2
    $\begingroup$ In the meantime, in Hörmander's book "Linear partial differential operators" (1963), Chapter V, §5.3 (page 123), you'll find a full proof of Holmgren's theorem. It is formulated differently from your reference, but the content of the theorem is the same. I can post this formulation as an answer, if you wish. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Aug 17, 2021 at 21:32
  • $\begingroup$ Thank you! I know this version of Holmgren's Theorem, as in Hörmander's book. I was looking for the original article more out of curiosity, I didn't even find Holmgren's profile on MathSciNet, just some papers published in the Mathematische Annalen. $\endgroup$
    – Math
    Aug 17, 2021 at 21:40
  • $\begingroup$ Also, I found a list of his publications: archive.ymsc.tsinghua.edu.cn/pacm_download/117/… $\endgroup$
    – Math
    Aug 17, 2021 at 21:41

1 Answer 1

Reset to default
12
$\begingroup$

The full text of the article can be found scanned here.

Improve this answer
$\endgroup$
3
  • $\begingroup$ Wow! I didn't expect someone to find it so quickly, I've been looking for a week! $\endgroup$
    – Math
    Aug 17, 2021 at 21:46
  • 2
    $\begingroup$ Thank you so much! $\endgroup$
    – Math
    Aug 17, 2021 at 21:49
  • 7
    $\begingroup$ We Swedes know where to find each other :-) $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Aug 17, 2021 at 21:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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