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Keywords:
Laplace equation; Neumann problem; potential; boundary integral equation method
Laplace equation; Neumann problem; potential; boundary integral equation method
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References:
[1] D. R. Adams, L. I. Hedberg: Function Spaces and Potential Theory. Grundlehren der mathematischen Wissenschaften 314. Springer-Verlag, Berlin-Heidelberg, 1995. MR 1411441
[2] D. H. Armitage, S. J. Gardiner: Classical Potential Theory. Springer-Verlag, London, 2001. MR 1801253
[3] J. Deny: Les potentiels d’énergie finie. Acta Math. 82 (1950), 107–183. MR 0036371 | Zbl 0034.36201
[4] L. E. Fraenkel: Introduction to Maximum Principles and Symmetry in Elliptic Problems. Cambridge University Press, Cambridge, 2000. MR 1751289 | Zbl 0947.35002
[5] L. L. Helms: Introduction to Potential Theory. Pure and Applied Mathematics 22. John Wiley & Sons, 1969. MR 0261018
[6] H. Heuser: Funktionalanalysis. Teubner, Stuttgart, 1975. MR 0482021 | Zbl 0309.47001
[7] S. Jerison, C. E. Kenig: Boundary behavior of harmonic functions in non-tangentially accessible domains. Adv. Math. 47 (1982), 80–147.
[8] P. W. Jones: Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147 (1981), 71–88. MR 0631089 | Zbl 0489.30017
[9] J. J. Koliha: A generalized Drazin inverse. Glasgow Math. J. 38 (1996), 367–381. MR 1417366 | Zbl 0897.47002
[10] P. Koskela, H. Tuominen: Measure density and extendability of Sobolev functions. (to appear).
[11] J. Král: Integral Operators in Potential Theory. Lecture Notes in Mathematics 823. Springer-Verlag, Berlin, 1980, pp. . MR 0590244
[12] N. L. Landkof: Fundamentals of Modern Potential Theory. Izdat. Nauka, Moscow, 1966. (Russian) MR 0214795
[13] V. G. Maz’ya, S. V. Poborchi: Differentiable Functions on Bad Domains. World Scientific Publishing, Singapore, 1997. MR 1643072
[14] W. McLean: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, 2000. MR 1742312 | Zbl 0948.35001
[15] D. Medková: Solution of the Robin problem for the Laplace equation. Appl. Math. 43 (1998), 133–155. MR 1609158
[16] D. Medková: Solution of the Neumann problem for the Laplace equation. Czechoslovak Math. J. 48 (1998), 768–784.
[17] C. Miranda: Differential Equations of Elliptic Type. Springer-Verlag, Berlin, 1970. MR 0284700 | Zbl 0198.14101
[18] I. Netuka: Smooth surfaces with infinite cyclic variation. Čas. Pěst. Mat. 96 (1971), 86–101. (Czech) MR 0284553 | Zbl 0204.08002
[19] M. Schechter: Principles of Functional Analysis. Am. Math. Soc., Providence, 2002. MR 1861991
[20] G. E. Shilov: Mathematical Analysis. Second Special Course. Nauka, Moskva, 1965. (Russian) MR 0219869
[21] Ch. G. Simader, H. Sohr: The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains. Pitman Research Notes in Mathematics Series 360. Addison Wesley Longman Inc., Essex, 1996. MR 1454361
[22] J. Stampfli: Hyponormal operators. Pacific J. Math. 12 (1962), 1453–1458. MR 0149282 | Zbl 0129.08701
[23] O. Steinbach, W. L. Wendland: On C. Neumann’s method for second-order elliptic systems in domains with non-smooth boundaries. J. Math. Anal. Appl. 262 (2001), 733–748. MR 1859336
[24] G. Verchota: Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains. J. Funct. Anal. 59 (1984), 572–611. MR 0769382 | Zbl 0589.31005
[25] K. Yosida: Functional Analysis. Springer-Verlag, Berlin, 1965. Zbl 0126.11504
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