| Title:
|
Continuous extendibility of solutions of the third problem for the Laplace equation (English) |
| Author:
|
Medková, Dagmar |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
669-688 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A necessary and sufficient condition for the continuous extendibility of a solution of the third problem for the Laplace equation is given. (English) |
| Keyword:
|
third problem |
| Keyword:
|
Laplace equation |
| Keyword:
|
continuous extendibility |
| MSC:
|
31B10 |
| MSC:
|
35B65 |
| MSC:
|
35J05 |
| MSC:
|
35J25 |
| idZBL:
|
Zbl 1080.35009 |
| idMR:
|
MR2000062 |
| . |
| Date available:
|
2009-09-24T11:05:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127832 |
| . |
| Reference:
|
[1] V. Anandam and M. A. Al-Gwaiz: Global representation of harmonic and biharmonic functions.Potential Anal. 6 (1997), 207–214. MR 1452543, 10.1023/A:1017908608650 |
| Reference:
|
[2] V. Anandam and M. Damlakhi: Harmonic singularity at infinity in $R^n$.Real Anal. Exchange 23 (1997/8), 471–476. MR 1639952 |
| Reference:
|
[3] T. S. Angell, R. E. Kleinman and J. Král: Layer potentials on boundaries with corners and edges.Čas. pěst. mat. 113 (1988), 387–402. MR 0981880 |
| Reference:
|
[4] Yu. D. Burago and V. G. Maz’ya: Potential theory and function theory for irregular regions.Zapiski Naučnyh Seminarov LOMI 3 (1967), 1–152 (In Russian). |
| Reference:
|
[5] L. E. Fraenkel: Introduction to Maximum Principles and Symmetry in Elliptic Problems. Cambridge Tracts in Mathematics 128.Cambridge University Press, 2000. MR 1751289 |
| Reference:
|
[6] N. V. Grachev and V. G. Maz’ya: On the Fredholm radius for operators of the double layer potential type on piecewise smooth boundaries.Vest. Leningrad. Univ. 19 (1986), 60–64. MR 0880678 |
| Reference:
|
[7] N. V. Grachev and V. G. Maz’ya: Invertibility of boundary integral operators of elasticity on surfaces with conic points.Report LiTH-MAT-R-91-50, Linköping Univ., Sweden, . |
| Reference:
|
[8] N. V. Grachev and V. G. Maz’ya: Solvability of a boundary integral equation on a polyhedron.Report LiTH-MAT-R-91-50, Linköping Univ., Sweden, . |
| Reference:
|
[9] N. V. Grachev and 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:
|
[10] L. L. Helms: Introduction to Potential Theory. Pure and Applied Mathematics 22.John Wiley & Sons, 1969. MR 0261018 |
| Reference:
|
[11] J. Král: Integral Operators in Potential Theory. Lecture Notes in Mathematics 823.Springer-Verlag, Berlin, 1980. MR 0590244 |
| Reference:
|
[12] J. Král: The Fredholm method in potential theory.Trans. Amer. Math. Soc. 125 (1966), 511–547. MR 0209503, 10.2307/1994580 |
| Reference:
|
[13] J. Král and W. L. Wendland: Some examples concerning applicability of the Fredholm-Radon method in potential theory.Aplikace matematiky 31 (1986), 293–308. MR 0854323 |
| Reference:
|
[14] N. L. Landkof: Fundamentals of Modern Potential Theory.Izdat. Nauka, Moscow, 1966. (Russian) MR 0214795 |
| Reference:
|
[15] D. Medková: The third boundary value problem in potential theory for domains with a piecewise smooth boundary.Czechoslovak Math. J. 47(122) (1997), 651–679. MR 1479311, 10.1023/A:1022818618177 |
| Reference:
|
[16] D. Medková: Solution of the Robin problem for the Laplace equation.Appl. Math. 43 (1998), 133–155. MR 1609158, 10.1023/A:1023267018214 |
| Reference:
|
[17] D. Medková: Solution of the Neumann problem for the Laplace equation.Czechoslovak Math. J. 48(123) (1998), 768–784. MR 1658269, 10.1023/A:1022447908645 |
| Reference:
|
[18] D. Medková: Continuous extendibility of solutions of the Neumann problem for the Laplace equation.Czechoslovak Math. J 53(128) (2003), 377–395. MR 1983459, 10.1023/A:1026239404667 |
| Reference:
|
[19] J. Nečas: Les méthodes directes en théorie des équations élliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[20] 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:
|
[21] I. Netuka: Generalized Robin problem in potential theory.Czechoslovak Math. J. 22(97) (1972), 312–324. Zbl 0241.31008, MR 0294673 |
| Reference:
|
[22] I. Netuka: An operator connected with the third boundary value problem in potential theory.Czechoslovak Math. J. 22(97) (1972), 462–489. Zbl 0241.31009, MR 0316733 |
| Reference:
|
[23] I. Netuka: The third boundary value problem in potential theory.Czechoslovak Math. J. 22(97) (1972), 554–580. Zbl 0242.31007, MR 0313528 |
| Reference:
|
[24] I. Netuka: Continuity and maximum principle for potentials of signed measures.Czechoslovak Math. J. 25(100) (1975), 309–316. Zbl 0309.31019, MR 0382690 |
| Reference:
|
[25] A. Rathsfeld: The invertibility of the double layer potential in the space of continuous functions defined on a polyhedron.The panel method. Appl. Anal. 45 (1992), 1–4, 135–177. MR 1293594, 10.1080/00036819208840093 |
| Reference:
|
[26] A. Rathsfeld: The invertibility of the double layer potential operator in the space of continuous functions defined over a polyhedron. The panel method. Erratum.Appl. Anal. 56 (1995), 109–115. Zbl 0921.31004, MR 1378015, 10.1080/00036819508840313 |
| Reference:
|
[27] G. E. Shilov: Mathematical analysis. Second special course.Nauka, Moskva, 1965. (Russian) MR 0219869 |
| Reference:
|
[28] Ch. G. Simader and H. Sohr: The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains.Pitman Research Notes in Mathematics Series 360, Addison Wesley Longman Inc., 1996. MR 1454361 |
| Reference:
|
[29] M. Schechter: Principles of Functional Analysis.Academic press, New York-London, 1973. MR 0467221 |
| Reference:
|
[30] W. P. Ziemer: Weakly Differentiable Functions.Springer Verlag, 1989. Zbl 0692.46022, MR 1014685 |
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