A mixed boundary value problem for the Laplace equation in an angle (1st part)

Alfredo Lorenzi

Rendiconti del Seminario Matematico della Università di Padova (1975)

  • Volume: 54, page 147-183
  • ISSN: 0041-8994

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Lorenzi, Alfredo. "A mixed boundary value problem for the Laplace equation in an angle (1st part)." Rendiconti del Seminario Matematico della Università di Padova 54 (1975): 147-183. <http://eudml.org/doc/107569>.

@article{Lorenzi1975,
author = {Lorenzi, Alfredo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {147-183},
publisher = {Seminario Matematico of the University of Padua},
title = {A mixed boundary value problem for the Laplace equation in an angle (1st part)},
url = {http://eudml.org/doc/107569},
volume = {54},
year = {1975},
}

TY - JOUR
AU - Lorenzi, Alfredo
TI - A mixed boundary value problem for the Laplace equation in an angle (1st part)
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1975
PB - Seminario Matematico of the University of Padua
VL - 54
SP - 147
EP - 183
LA - eng
UR - http://eudml.org/doc/107569
ER -

References

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  1. [1] A. Avantaggiati - M. Troisi, Spazi di Sobolev con peso e problemi ellittici in un angolo - I, Ann. Mat. Pura Appl., 95 (1973), pp. 361-408; II, Ann. Mat. Pura Appl., 97 (1973), pp. 207-252; III, Ann. Mat. Pura Appl., 99 (1974), pp. 1-64. Zbl0274.35033MR331039
  2. [2] C. Baiocchi - V. Comincioli - E. Magenes - G.A. Pozzi, Free boundary problems in the theory of fluid flow through porous media: existence and uniqueness theorems, Ann. Mat. Pura Appl., 97 (1973), pp. 1-82. Zbl0343.76036MR342026
  3. [3] P. Grisvard, Problème de Dirichlet dans un cone, Ricerche Mat., 20 (1971), pp. 175-192. Zbl0233.35024MR346308
  4. [4] P. Grisvard, Alternative de Fredholm relative au problème de Dirichlet dans un polygone ou un polyèdre, Boll. Un. Mat. Ital. (4), 5 (1972), pp. 132-164. Zbl0277.35035MR312068
  5. [5] P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 5 (1972) pp. 637-729. Zbl0272.46025MR341059
  6. [6] Hardy - Littlewood - Polya, Inequalities, Cambridge (1964). Zbl0010.10703
  7. [7] A. Lorenzi, A mixed problem for the Laplace equation in a right angle with an oblique derivative given on a side of the angle, Ann. Mat. Pura Appl., 100 (1974), pp. 259-306 Zbl0289.35024MR367436
  8. [8] M. Merigot, Régularité de dérivées de la solution du problème de Dirichlet dans un secteur plan, Matematiche, 27 (1972), pp. 324-359. Zbl0277.35027MR346295
  9. [9] M. Merigot, Etude du problème Δu = f dans un polygone plan. Inegalités a prioriBoll. Un. Mat. Ital. (4) 10 (1974), pp. 577-597. Zbl0308.35015
  10. [10] N.I. Muskhelishvili, Singular integral equations, P. Noordhoff (1953). Zbl0108.29203MR355494
  11. [11] M.P. Van Ouverkerk - DIJKERS, Solutions of the equation of Helmholtz in a quarter plane with an oblique boundary condition, Mathematisch CentrumAmsterdam (1970). Zbl0204.11201
  12. [12] J. Peetre, Espaces d'interpolation et théorème de Sobolev, Ann. Inst. Fourier Grenoble, 16, 1 (1966), pp. 279-317. Zbl0151.17903MR221282
  13. [13] E. Shamir, Mixed boundary value problems for elliptic equations in the plane. The Lp theory, Ann. Scuola Norm. Sup. Pisa, 17 (1963), pp. 117-139. Zbl0117.07002MR157089
  14. [14] E. Shamir, Reduced Hilbert transforms and singular integral equationsJ. Analyse Math., 12 (1964), pp. 277-305. Zbl0173.14502MR165328
  15. [15] E.C. Titchmarsh, Theory of Fourier integrals (Oxford University Press (1937). Zbl0017.40404JFM63.0367.05
  16. [16] E.A. Volkov, Differentiability properties of solutions of boundary value problems for the Laplace equation on a polygon, Trudy Mat. Inst. Steklov, 77 (1965), pp. 113-142; English translation: Proc. Steklov Inst, Math. (1967), pp. 127-159. Zbl0162.16701MR192078

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