| Title:
|
The boundary-value problems for Laplace equation and domains with nonsmooth boundary (English) |
| Author:
|
Medková, Dagmar |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
173-181 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed. (English) |
| Keyword:
|
Laplace equation |
| Keyword:
|
Dirichlet problem |
| Keyword:
|
Neumann problem |
| Keyword:
|
Robin problem |
| MSC:
|
31B05 |
| MSC:
|
31B10 |
| MSC:
|
35J05 |
| MSC:
|
35J25 |
| idZBL:
|
Zbl 0910.35038 |
| idMR:
|
MR1629696 |
| . |
| Date available:
|
2009-02-17T10:10:59Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107642 |
| . |
| Reference:
|
[1] R. S. Angell R. E. Kleinman J. Král: Layer potentials on boundaries with corners and edges.Čas. pěst. mat., 113 (1988), 387–402. MR 0981880 |
| Reference:
|
[2] Yu. D. Burago V. G. Maz’ ya: Potential theory and function theory for irregular regions.Seminars in mathematics V. A. Steklov Mathematical Institute, Leningrad, 1969. MR 0240284 |
| Reference:
|
[3] N. V. Grachev V. G. Maz’ya: On the Fredholm radius for operators of the double layer potential type on piecewise smooth boundaries.Vest. Leningrad. Univ., 19 (4), 1986, 60–64. MR 0880678 |
| Reference:
|
[4] N. V. Grachev V. G. Maz’ya: Estimates for kernels of the inverse operators of the integral equations of elasticity on surfaces with conic points.Report LiTH-MAT-R-91-06, Linköping Univ., Sweden. |
| Reference:
|
[5] N. V. Grachev V. G. Maz’ya: Invertibility of boundary integral operators of elasticity on surfaces with conic points.Report LiTH-MAT-R-91-07, Linköping Univ., Sweden. |
| Reference:
|
[6] N. V. Grachev V. G. Maz’ya: Solvability of a boundary integral equation on a polyhedron.Report LiTH-MAT-R-91-50, Linköping Univ., Sweden. |
| Reference:
|
[7] M. Chlebík: Tricomi Potentials.Thesis, Mathematical Institute of the Czechoslovak Academy of Sciences, Praha 1988 (in Slovak). |
| Reference:
|
[8] J. Král: On double-layer potential in multidimensional space.Dokl. Akad. Nauk SSSR, 159 (1964). MR 0176210 |
| Reference:
|
[9] J. Král: Integral Operators in Potential Theory.Lecture Notes in Mathematics 823, Springer-Verlag, Berlin, 1980. MR 0590244 |
| Reference:
|
[10] J. Král: The Fredholm method in potential theory.Trans. Amer. Math. Soc., 125 (1966), 511–547. MR 0209503 |
| Reference:
|
[11] J. Král I. Netuka: Contractivity of C. Neumann’s operator in potential theory.Journal of the Mathematical Analysis and its Applications, 61 (1977), 607–619. MR 0508010 |
| Reference:
|
[12] J. Král W. L. Wendland: Some examples concerning applicability of the Fredholm-Radon method in potential heory.Aplikace matematiky, 31 (1986), 239–308. MR 0854323 |
| Reference:
|
[13] R. Kress G. F. Roach: On the convergence of successive approximations for an integral equation in a Green’s function approach to the Dirichlet problem.Journal of mathematical analysis and applications, 55 (1976), 102–111. MR 0411214 |
| Reference:
|
[14] V. Maz’ya A. Solov’ev: On the boundary integral equation of the Neumann problem in a domain with a peak.Amer. Math. Soc. Transl., 155 (1993), 101–127. |
| Reference:
|
[15] D. Medková: The third boundary value problem in potential theory for domains with a piecewise smooth boundary.Czech. Math. J., 47 (1997), 651–679. MR 1479311 |
| Reference:
|
[16] D. Medková : Solution of the Neumann problem for the Laplace equation.Czech. Math. J. (in print). |
| Reference:
|
[17] D. Medková: Solution of the Robin problem for the Laplace equation.preprint No.120, Academy of Sciences of the Czech republic, 1997. MR 1609158 |
| Reference:
|
[18] I. Netuka: Smooth surfaces with infinite cyclic variation.Čas. pěst. mat., 96 (1971). Zbl 0204.08002, MR 0284553 |
| Reference:
|
[19] I. Netuka: The Robin problem in potential theory.Comment. Math. Univ. Carolinae, 12 (1971), 205–211. Zbl 0215.42602, MR 0287021 |
| Reference:
|
[20] I. Netuka: Generalized Robin problem in potential theory.Czech. Math. J., 22 (97) (1972), 312–324. Zbl 0241.31008, MR 0294673 |
| Reference:
|
[21] I. Netuka: An operator connected with the third boundary value problem in potential theory.Czech Math. J., 22 (97) (1972), 462–489. Zbl 0241.31009, MR 0316733 |
| Reference:
|
[22] I. Netuka: The third boundary value problem in potential theory.Czech. Math. J., 2 (97) (1972), 554–580. Zbl 0242.31007, MR 0313528 |
| Reference:
|
[23] I. Netuka: Fredholm radius of a potential theoretic operator for convex sets.Čas. pěst. mat., 100 (1975), 374–383. Zbl 0314.31006, MR 0419794 |
| Reference:
|
[24] C. Neumann: Untersuchungen über das logarithmische und Newtonsche Potential.Teubner Verlag, Leipzig, 1877. |
| Reference:
|
[25] C. Neumann: Zur Theorie des logarithmischen und des Newtonschen Potentials.Berichte über die Verhandlungen der Königlich Sachsischen Gesellschaft der Wissenschaften zu Leipzig, 22, 1870, 49–56, 264–321. |
| Reference:
|
[26] C. Neumann: Über die Methode des arithmetischen Mittels.Hirzel, Leipzig, 1887 (erste Abhandlung), 1888 (zweite Abhandlung). |
| Reference:
|
[27] J. Radon: Über Randwertaufgaben beim logarithmischen Potential.Sitzber. Akad. Wiss. Wien, 128, 1919, 1123–1167. |
| Reference:
|
[28] A. Rathsfeld: The invertibility of the double layer potential in the space of continuous functions defined on a polyhedron. The panel method.Applicable Analysis, 45, (1992), 1–4, 135–177. MR 1293594 |
| Reference:
|
[29] A. Rathsfeld: The invertibility of the double layer potential in the space of continuous functions defined on a polyhedron. The panel method. Erratum.Applicable Analysis, 56 (1995), 109–115. MR 1378015 |
| . |
