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.

  • 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. $\endgroup$ Aug 17, 2021 at 21:23
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    $\begingroup$ 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. $\endgroup$ 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


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

  • $\begingroup$ 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
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    $\begingroup$ Thank you so much! $\endgroup$
    – Math
    Aug 17, 2021 at 21:49
  • 7
    $\begingroup$ We Swedes know where to find each other :-) $\endgroup$ Aug 17, 2021 at 21:51

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