Continuous extendibility of solutions of the third problem for the Laplace equation

Dagmar Medková

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 669-688
  • ISSN: 0011-4642

Abstract

top
A necessary and sufficient condition for the continuous extendibility of a solution of the third problem for the Laplace equation is given.

How to cite

top

Medková, Dagmar. "Continuous extendibility of solutions of the third problem for the Laplace equation." Czechoslovak Mathematical Journal 53.3 (2003): 669-688. <http://eudml.org/doc/30808>.

@article{Medková2003,
abstract = {A necessary and sufficient condition for the continuous extendibility of a solution of the third problem for the Laplace equation is given.},
author = {Medková, Dagmar},
journal = {Czechoslovak Mathematical Journal},
keywords = {third problem; Laplace equation; continuous extendibility; third problem; Laplace equation; continuous extendibility},
language = {eng},
number = {3},
pages = {669-688},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuous extendibility of solutions of the third problem for the Laplace equation},
url = {http://eudml.org/doc/30808},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Medková, Dagmar
TI - Continuous extendibility of solutions of the third problem for the Laplace equation
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 669
EP - 688
AB - A necessary and sufficient condition for the continuous extendibility of a solution of the third problem for the Laplace equation is given.
LA - eng
KW - third problem; Laplace equation; continuous extendibility; third problem; Laplace equation; continuous extendibility
UR - http://eudml.org/doc/30808
ER -

References

top
  1. 10.1023/A:1017908608650, Potential Anal. 6 (1997), 207–214. (1997) MR1452543DOI10.1023/A:1017908608650
  2. Harmonic singularity at infinity in  R n , Real Anal. Exchange 23 (1997/8), 471–476. (1997/8) MR1639952
  3. Layer potentials on boundaries with corners and edges, Čas. pěst. mat. 113 (1988), 387–402. (1988) MR0981880
  4. Potential theory and function theory for irregular regions, Zapiski Naučnyh Seminarov LOMI 3 (1967), 1–152 (In Russian). (1967) 
  5. Introduction to Maximum Principles and Symmetry in Elliptic Problems. Cambridge Tracts in Mathematics 128, Cambridge University Press, 2000. (2000) MR1751289
  6. On the Fredholm radius for operators of the double layer potential type on piecewise smooth boundaries, Vest. Leningrad. Univ. 19 (1986), 60–64. (1986) MR0880678
  7. Invertibility of boundary integral operators of elasticity on surfaces with conic points, Report LiTH-MAT-R-91-50, Linköping Univ., Sweden, . 
  8. Solvability of a boundary integral equation on a polyhedron, Report LiTH-MAT-R-91-50, Linköping Univ., Sweden, . 
  9. 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, . 
  10. Introduction to Potential Theory. Pure and Applied Mathematics 22, John Wiley & Sons, 1969. (1969) MR0261018
  11. Integral Operators in Potential Theory. Lecture Notes in Mathematics 823, Springer-Verlag, Berlin, 1980. (1980) MR0590244
  12. 10.2307/1994580, Trans. Amer. Math. Soc. 125 (1966), 511–547. (1966) MR0209503DOI10.2307/1994580
  13. Some examples concerning applicability of the Fredholm-Radon method in potential theory, Aplikace matematiky 31 (1986), 293–308. (1986) MR0854323
  14. Fundamentals of Modern Potential Theory, Izdat. Nauka, Moscow, 1966. (Russian) (1966) MR0214795
  15. 10.1023/A:1022818618177, Czechoslovak Math.  J. 47(122) (1997), 651–679. (1997) MR1479311DOI10.1023/A:1022818618177
  16. 10.1023/A:1023267018214, Appl. Math. 43 (1998), 133–155. (1998) MR1609158DOI10.1023/A:1023267018214
  17. 10.1023/A:1022447908645, Czechoslovak Math.  J. 48(123) (1998), 768–784. (1998) MR1658269DOI10.1023/A:1022447908645
  18. 10.1023/A:1026239404667, Czechoslovak Math.  J 53(128) (2003), 377–395. (2003) MR1983459DOI10.1023/A:1026239404667
  19. Les méthodes directes en théorie des équations élliptiques, Academia, Prague, 1967. (1967) MR0227584
  20. Fredholm radius of a potential theoretic operator for convex sets, Čas. pěst. mat. 100 (1975), 374–383. (1975) Zbl0314.31006MR0419794
  21. Generalized Robin problem in potential theory, Czechoslovak Math.  J. 22(97) (1972), 312–324. (1972) Zbl0241.31008MR0294673
  22. An operator connected with the third boundary value problem in potential theory, Czechoslovak Math.  J. 22(97) (1972), 462–489. (1972) Zbl0241.31009MR0316733
  23. The third boundary value problem in potential theory, Czechoslovak Math.  J. 22(97) (1972), 554–580. (1972) Zbl0242.31007MR0313528
  24. Continuity and maximum principle for potentials of signed measures, Czechoslovak Math.  J. 25(100) (1975), 309–316. (1975) Zbl0309.31019MR0382690
  25. 10.1080/00036819208840093, The panel method. Appl. Anal. 45 (1992), 1–4, 135–177. (1992) MR1293594DOI10.1080/00036819208840093
  26. 10.1080/00036819508840313, Appl. Anal. 56 (1995), 109–115. (1995) Zbl0921.31004MR1378015DOI10.1080/00036819508840313
  27. Mathematical analysis. Second special course, Nauka, Moskva, 1965. (Russian) (1965) MR0219869
  28. The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains, Pitman Research Notes in Mathematics Series 360, Addison Wesley Longman Inc., 1996. (1996) MR1454361
  29. Principles of Functional Analysis, Academic press, New York-London, 1973. (1973) MR0467221
  30. Weakly Differentiable Functions, Springer Verlag, 1989. (1989) Zbl0692.46022MR1014685

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.