Abstract
In this chapter we intend to point out various questions briefly, which have been postponed until now, regarding both elliptic equations of second order and those of higher order and systems of equations. Many of these questions have great importance. Still it is not possible here, given the character of this volume, to give them a detailed and systematic treatment. Consequently we shall limit ourselves here to reporting the arguments to which this research refers and to giving, when it is possible, some indication of the method followed. In all this, we shall scarcely ever enter into the details either of the statements or of the proofs. In other words, in this chapter we wish only to classify, in some way, the bibliographic material collected at the end of the volume and upon which we have not touched until now.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
Picard, É.: Sur une équation aux dérivées partielles du second ordre relative à une surface fermée, correspondant à un équilibre calorifique. Ann. Éc. N. Sup. 26 (1909) 9–17.
Weyl, H.: Über die Bestimmung einer geschlossenen Fläche durch ihr Linienelement. Vierteljahrsschrift natur. Ges. Zürich 61 (1916) 40–72.
L. Hörmander: On the regularity of the solutions of boundary value problems, Acta Math. 99 (1958)225–264.
I. C. Gohberg and M. G. Krein : The basic propositions on defect numbers, root numbers, and indices of linear operators. Usp. Mat. Nauk 12 no. 1 (1957) 43–118; English transl. Amer. Math. Soc. (2) 13 (1960) 185–264.
L. van Howe : Sur éxtension de la condition de Legendre du calcul des variations aux intégrales multiples à plusieures fonctions inconnues. Indag. Math. 9 (1947) 3–8.
Almansi, E.: Sulintegrazione del equazione 2n u= 0. Ann. Mat. pura appl. 2 (1899) 1–51.
Boggio, T.: Sulla deformazione delle piastre elastiche soggette al calore. Atti Acc. Sci. Torino 40 (1904/5) 219–240.
Lauricella, G.: Integrazione del equazione 2 (2 ) = 0. Atti Acc. Sci. Torino 31 (1895/1896) 1010–1018.
Hadamard, J.: Sur équilibre des plaques élastiques circulaires libres ou appuyées et celui de la sphère isotrope. Ann. Éc. N. Sup. 18 (1901) 313–342.
Volterra, V.: Osservazioni sulla nota precendente del Prof. Lauricella e sopra una nota di analogo argomento del Ing. Almansi. Atti Acc. Sci. Torino 31 (1895/1896) 1018–1021.
Boggio, T.: Sulle funzioni di Green di ordine m. Rend. Circ. Mat. Palermo 20 (1905) 97–135.
Hadamard, J.: Mémoire sur le problème analyse relativ à équilibre des plaques élastiques encastrées. Mém. Acad. Sci. Paris 33 (1908) 9–22.
Lauricella, G.: Sur intégration de équation relative à équilibre des plaques élastiques encastrées. Acta Math. 32 (1909) 201–256.
Korn, A.: Sur équilibre des plaques élastiques encastrées. Ann. Ec. N. Sup. 25 (1908) 529–583.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1970 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Miranda, C. (1970). Other research on equations of second order. Equations of higher order. Systems of equations.. In: Partial Differential Equations of Elliptic Type. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87773-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-87773-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-87775-9
Online ISBN: 978-3-642-87773-5
eBook Packages: Springer Book Archive