L’énoncé et la preuve du théorème B dans [BZ20] ne sont pas complets, sauf dans le cas où la donnée au bord s’annule identiquement. Nous donnons ici la version correcte de l’énoncé ainsi qu’une démonstration complète.
The statement and the proof of Theorem B in [BZ20] are not complete, except when the boundary datum vanishes identically. We give here the correct version of the statement as well as a complete proof.
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Keywords: Complex Monge-Ampère equations, complex Hessian equations, Dirichlet problem, obstacle problems, maximal subextension, capacity.
Mot clés : Équations de Monge-Ampère complexes, équations hessienne complexes, problème de Dirichlet, problèmes d’obstacle, sous-extension maximale, capacités hessiennes
@article{JEP_2021__8__779_0, author = {Benali, Amel and Zeriahi, Ahmed}, title = {Erratum to {{\textquotedblleft}The} {H\"older} continuous subsolution theorem for complex {Hessian} equations{\textquotedblright}}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {779--789}, publisher = {Ecole polytechnique}, volume = {8}, year = {2021}, doi = {10.5802/jep.157}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jep.157/} }
TY - JOUR AU - Benali, Amel AU - Zeriahi, Ahmed TI - Erratum to “The Hölder continuous subsolution theorem for complex Hessian equations” JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 779 EP - 789 VL - 8 PB - Ecole polytechnique UR - http://archive.numdam.org/articles/10.5802/jep.157/ DO - 10.5802/jep.157 LA - en ID - JEP_2021__8__779_0 ER -
%0 Journal Article %A Benali, Amel %A Zeriahi, Ahmed %T Erratum to “The Hölder continuous subsolution theorem for complex Hessian equations” %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 779-789 %V 8 %I Ecole polytechnique %U http://archive.numdam.org/articles/10.5802/jep.157/ %R 10.5802/jep.157 %G en %F JEP_2021__8__779_0
Benali, Amel; Zeriahi, Ahmed. Erratum to “The Hölder continuous subsolution theorem for complex Hessian equations”. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 779-789. doi : 10.5802/jep.157. http://archive.numdam.org/articles/10.5802/jep.157/
[BZ20] The Hölder continuous subsolution theorem for complex Hessian equations, J. Éc. polytech. Math., Volume 7 (2020), pp. 981-1007 | DOI | Zbl
[GKZ08] Hölder continuous solutions to Monge-Ampére equations, Bull. London Math. Soc., Volume 40 (2008) no. 6, pp. 1070-1080 | DOI | Zbl
[Lu12] Équations hessiennes complexes, Ph. D. Thesis, Université de Toulouse 3 (2012) | theses.fr
[Ngu12] Subsolution theorem for the complex Hessian equation, Univ. Iagel. Acta Math., Volume 50 (2012), pp. 69-88 | MR | Zbl
[Zer20] Remarks on the modulus of continuity of subharmonic functions, 2020 | arXiv
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