Boundary integral equations of the logarithmic potential theory for domains with peaks

Alexander A. Soloviev

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1995)

  • Volume: 6, Issue: 4, page 211-236
  • ISSN: 1120-6330

Abstract

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Integral equations of boundary value problems of the logarithmic potential theory for a plane domain with several peaks at the boundary are studied. We present theorems on the unique solvability and asymptotic representations for solutions near peaks. We also find kernels of the integral operators in a class of functions with a weak power singularity and describe classes of uniqueness.

How to cite

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Soloviev, Alexander A.. "Boundary integral equations of the logarithmic potential theory for domains with peaks." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 6.4 (1995): 211-236. <http://eudml.org/doc/244221>.

@article{Soloviev1995,
abstract = {Integral equations of boundary value problems of the logarithmic potential theory for a plane domain with several peaks at the boundary are studied. We present theorems on the unique solvability and asymptotic representations for solutions near peaks. We also find kernels of the integral operators in a class of functions with a weak power singularity and describe classes of uniqueness.},
author = {Soloviev, Alexander A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Boundary integral equation; Logarithmic potential; Asymptotics of solution; nonsmooth domain; single layer potential; double layer potentials; unique solvability; asymptotic representations near peaks},
language = {eng},
month = {12},
number = {4},
pages = {211-236},
publisher = {Accademia Nazionale dei Lincei},
title = {Boundary integral equations of the logarithmic potential theory for domains with peaks},
url = {http://eudml.org/doc/244221},
volume = {6},
year = {1995},
}

TY - JOUR
AU - Soloviev, Alexander A.
TI - Boundary integral equations of the logarithmic potential theory for domains with peaks
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1995/12//
PB - Accademia Nazionale dei Lincei
VL - 6
IS - 4
SP - 211
EP - 236
AB - Integral equations of boundary value problems of the logarithmic potential theory for a plane domain with several peaks at the boundary are studied. We present theorems on the unique solvability and asymptotic representations for solutions near peaks. We also find kernels of the integral operators in a class of functions with a weak power singularity and describe classes of uniqueness.
LA - eng
KW - Boundary integral equation; Logarithmic potential; Asymptotics of solution; nonsmooth domain; single layer potential; double layer potentials; unique solvability; asymptotic representations near peaks
UR - http://eudml.org/doc/244221
ER -

References

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  1. MAZ'YA, V., Boundary Integral Equations. Encyclopedia of Mathematical Sciences, Springer-Verlag, Berlin-Heidelberg1991. Zbl0780.45002MR1098507DOI10.1007/978-3-642-58175-5_2
  2. RADON, J., Über die Randwertaufgaben beim logarithmischen Potential. S.-B. Akad. Wiss. Wien Math.-Nat. Kl, 128, 1919; Abt. IIa, 1123-1167. JFM47.0457.01
  3. MAZ'YA, V. - SOLOVIEV, A. A., On the integral equation of the Dirichlet problem in a plane domain with peaks at the boundary. Matem. Sbornik, 180, n. 9, 1989, 1211-1233; English transl. in Math. USSR Sbornik, vol. 68, n. 1, 1991, 61-83. Zbl0683.45002MR1017822
  4. MAZ'YA, V. - SOLOVIEV, A. A., On the boundary integral equation of the Neumann problem in a domain with a peak. Trudy Leningrad. Mat. Ob., 1, 1990, 109-134; English transl. in Amer. Math. Soc. Transl., 155(2), 1993, 101-127. Zbl0796.45003MR1104208
  5. KONDRATIEV, V. A., Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Ob., 16, 1967, 209-292; English transl. in Trans. Moscow Math. Soc., 16, 1967, 227-313. Zbl0194.13405MR226187
  6. STOILOV, S., Theory of Functions of a Complex Variable. Edit. Acad. Rep. Pop. Romaine, Bucharest1954. 
  7. SMIRNOV, V. I. - LEBEDEV, N. A., Constructive Theory of Functions of a Complex Variable. M.I.T. Press, Cambridge, Massachusetts1968. Zbl0164.37503MR229803

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