The multiple 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 (1992)

  • Volume: 3, Issue: 4, page 241-259
  • ISSN: 1120-6330

Abstract

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The definition of multiple layer potential for the biharmonic equation in R n is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.

How to cite

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Cialdea, Alberto. "The multiple 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 3.4 (1992): 241-259. <http://eudml.org/doc/244277>.

@article{Cialdea1992,
abstract = {The definition of multiple layer potential for the biharmonic equation in \( \mathbb\{R\}^\{n\} \) is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.},
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 systems; Potential theory; Biharmonic problem; multiple layer potential for the biharmonic equation; Dirichlet problem; singular integral system},
language = {eng},
month = {12},
number = {4},
pages = {241-259},
publisher = {Accademia Nazionale dei Lincei},
title = {The multiple layer potential for the biharmonic equation in \( n \) variables},
url = {http://eudml.org/doc/244277},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Cialdea, Alberto
TI - The multiple 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 - 1992/12//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 4
SP - 241
EP - 259
AB - The definition of multiple layer potential for the biharmonic equation in \( \mathbb{R}^{n} \) is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.
LA - eng
KW - Singular integral systems; Potential theory; Biharmonic problem; multiple layer potential for the biharmonic equation; Dirichlet problem; singular integral system
UR - http://eudml.org/doc/244277
ER -

References

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  1. AGMON, S., Multiple Layer Potential and the Dirichlet Problem for Higher Order Elliptic Equations in the Plane. Comm. Pure Appl. Math., X, 1957, 179-239. Zbl0081.09801MR106323
  2. CIALDEA, A., Sul problema della derivata obliqua per le funzioni armoniche e questioni connesse. Rend. Acc. Naz. delle Scienze detta dei XL, 12, 1988, 181-200. Zbl0676.35017
  3. CIALDEA, A., The simple layer potential for the biharmonic equation in n variables. Rend. Mat. Acc. Lincei, s. 9, vol. 2, 1991, 115-127. Zbl0734.31007MR1120131
  4. CIALDEA, A., A multiple layer potential theory alternative to Agmons. Arch. Rat. Mech. Anal., to appear. Zbl0781.31007
  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 Academy of Sciences and Humanities, Pergamon Press, Oxford1961, 175-226. Zbl0126.17801MR133434
  7. FICHERA, G., Operatori di Riesz-Fredholm, operatori riducibili, equazioni integrali singolari, applicazioni. Pubbl. dell'Ist. Matem. dell'Univ. di Roma, 1963. 
  8. FICHERA, G., Generalized biharmonic problem and related eigenvalue problems. In: Blanch Anniversary Volume. Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, 1967, 37-44. Zbl0185.19402MR214940
  9. FICHERA, G., The problem of the completeness of systems of particular solutions of partial differential equations. Numerical Math., ISNM49, Birkhäuser Verlag, Basel1979, 25-41. Zbl0434.35010MR564084
  10. FICHERA, G. - DE VITO, L., Funzioni analitiche di una variabile complessa. 3a ed., Veschi, Roma1971. Zbl0226.30001
  11. HODGE, W. V., A Dirichlet problem for harmonic functionals with applications to analytic varieties. Proc. of the London Math. Soc., 2, 36, 1934, 257-303. Zbl0008.02203MR1575963DOI10.1112/plms/s2-36.1.257
  12. V. D. KUPRADZE (ed.), Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam1979. Zbl0406.73001MR530377
  13. MIKHLIN, S. G. - PRÖSSDORF, S., Singular Integral Operators. Springer-Verlag, Berlin1986. Zbl0612.47024MR867687DOI10.1007/978-3-642-61631-0

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