In a domain with corners, we prove that by acting on an arbitrarily small part of the domain or on a small part of the boundary, we obtain a regular solution of the Laplace equation.
On montre que, dans un domaine à coins, par une action sur une petite partie du domaine ou sur une petite partie de la frontière, on obtient une solution régulière de l'équation de Laplace.
Accepted:
Published online:
@article{CRMATH_2006__343_2_115_0, author = {Niane, Mary Teuw and Bayili, Gilbert and S\`ene, Abdoulaye and S\`ene, Abdou and Sy, Mamadou}, title = {Is it possible to cancel singularities in a domain with corners and cracks?}, journal = {Comptes Rendus. Math\'ematique}, pages = {115--118}, publisher = {Elsevier}, volume = {343}, number = {2}, year = {2006}, doi = {10.1016/j.crma.2006.05.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.05.003/} }
TY - JOUR AU - Niane, Mary Teuw AU - Bayili, Gilbert AU - Sène, Abdoulaye AU - Sène, Abdou AU - Sy, Mamadou TI - Is it possible to cancel singularities in a domain with corners and cracks? JO - Comptes Rendus. Mathématique PY - 2006 SP - 115 EP - 118 VL - 343 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.05.003/ DO - 10.1016/j.crma.2006.05.003 LA - en ID - CRMATH_2006__343_2_115_0 ER -
%0 Journal Article %A Niane, Mary Teuw %A Bayili, Gilbert %A Sène, Abdoulaye %A Sène, Abdou %A Sy, Mamadou %T Is it possible to cancel singularities in a domain with corners and cracks? %J Comptes Rendus. Mathématique %D 2006 %P 115-118 %V 343 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2006.05.003/ %R 10.1016/j.crma.2006.05.003 %G en %F CRMATH_2006__343_2_115_0
Niane, Mary Teuw; Bayili, Gilbert; Sène, Abdoulaye; Sène, Abdou; Sy, Mamadou. Is it possible to cancel singularities in a domain with corners and cracks?. Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 115-118. doi : 10.1016/j.crma.2006.05.003. http://archive.numdam.org/articles/10.1016/j.crma.2006.05.003/
[1] Singularities in Boundary Value Problems, Masson, 1992
[2] Linear Partial Differential Operators, Springer-Verlag, 1976
[3] Boundary value problems for elliptic equations in domains with conical or angular points, Transactions Moscow Mat. Soc. (1967), pp. 227-313
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