The simple layer potential for the biharmonic equation in n variables

Alberto Cialdea

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 2, page 115-127
  • ISSN: 1120-6330

Abstract

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A theory of the «simple layer potential» for the classical biharmonic problem in R n is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with n scalar components into a vector whose components are n differential forms of degree one.

How to cite

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Cialdea, Alberto. "The simple layer potential for the biharmonic equation in \( n \) variables." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.2 (1991): 115-127. <http://eudml.org/doc/244337>.

@article{Cialdea1991,
abstract = {A theory of the «simple layer potential» for the classical biharmonic problem in \( \mathbb\{R\}^\{n\} \) is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with \( n \) scalar components into a vector whose components are \( n \) differential forms of degree one.},
author = {Cialdea, Alberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Singular integral operators; Differential forms; Biharmonic problem; biharmonic; simple layer potential; singular integral operators},
language = {eng},
month = {6},
number = {2},
pages = {115-127},
publisher = {Accademia Nazionale dei Lincei},
title = {The simple layer potential for the biharmonic equation in \( n \) variables},
url = {http://eudml.org/doc/244337},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Cialdea, Alberto
TI - The simple layer potential for the biharmonic equation in \( n \) variables
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/6//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 2
SP - 115
EP - 127
AB - A theory of the «simple layer potential» for the classical biharmonic problem in \( \mathbb{R}^{n} \) is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with \( n \) scalar components into a vector whose components are \( n \) differential forms of degree one.
LA - eng
KW - Singular integral operators; Differential forms; Biharmonic problem; biharmonic; simple layer potential; singular integral operators
UR - http://eudml.org/doc/244337
ER -

References

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  2. CIALDEA, A., Elastostatics with non absolutely continuous data. J. Elas., 23, 1990, 13-51. Zbl0723.73023MR1065229DOI10.1007/BF00041683
  3. DE VITO, L., Esistenza di un particolare integrale singolare sopra una superficie. Atti Acc. Lincei Mem. fis., s. 8, vol. 7, 1963, 61-90. Zbl0131.10904MR170115
  4. FICHERA, G., On some general integration methods employed in connection with linear differential equations. J. Math. and Phys., 29, 1950, 59-68. Zbl0038.05902MR39163
  5. FICHERA, G., Una introduzione alla teoria delle equazioni integrali singolari. Rend. Matem. Roma, (5), 17, 1958, 82-191. Zbl0097.08602MR106328
  6. FICHERA, G., Spazi lineari di k -misure e di forme differenziali. Proceedings of Intern. Symposium on Linear Spaces (Jerusalem 1960), Israel Ac. of Sciences and Humanities, Pergamon Press, Oxford1961, 175-226. Zbl0126.17801MR133434
  7. FICHERA, G., Linear elliptic equations of higher order in two independent variables and singular integral equations, with applications to anisotropic inhomogeneous elasticity. In: R. E. LANGER (éd.), Partial Differential Equations and Continuum Mechanics, Madison, 1961, 55-80. Zbl0111.29602MR156084
  8. FICHERA, G., Operatori di Riesz-Fredholm, operatori riducibili, equazioni integrali singolari, applicazioni. Pubbl. dell'Ist. Matem. dell'Univ. di Roma, 1963. 
  9. FICHERA, G., Linear Elliptic Differential Systems and Eigenvalue Problems. Lecture notes in mathematics, vol. 8, Springer, Berlin-Heidelberg-New York1965. Zbl0138.36104MR209639
  10. V. D. KUPRADZE (éd.), Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam1979. Zbl0406.73001MR530377
  11. MIKHLIN, S. G., Multidimensional Singular Integrals and Integral Equations. Pergamon Press, Oxford1965. Zbl0129.07701MR185399
  12. MUSKHELISHVILI, N. I., Singular integral equations. Noordhoff, Groningen1972 (reprinted). Zbl0174.16201MR355494
  13. PICONE, M., Nuovi indirizzi di ricerca nella teoria e nel calcolo delle soluzioni di talune equazioni lineari alle derivate parziali della fisica-matematica. Ann. Sc. Sup. Pisa, (2), 5, 1936, 213-288. MR1556776JFM62.0564.04

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