Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation
We examine a semi-linear variant of the bi-Laplacian equation in the superlinear, subquadratic setting and obtain $C^{2,\sigma }$-regularity estimates, depending on the growth regime of the nonlinearity. Our strategy is to render this fourth-order problem as a system of two Poisson equations and exp...
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Académie des sciences
2025-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.737/ |
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| author | Alcantara, Claudemir Pimentel, Edgard Urbano, José Miguel |
| author_facet | Alcantara, Claudemir Pimentel, Edgard Urbano, José Miguel |
| author_sort | Alcantara, Claudemir |
| collection | DOAJ |
| description | We examine a semi-linear variant of the bi-Laplacian equation in the superlinear, subquadratic setting and obtain $C^{2,\sigma }$-regularity estimates, depending on the growth regime of the nonlinearity. Our strategy is to render this fourth-order problem as a system of two Poisson equations and explore the interplay between the integrability and smoothness available for each equation taken isolated. |
| format | Article |
| id | doaj-art-df9c2cf283f048d3b96b6a1a64676d5c |
| institution | Matheson Library |
| issn | 1778-3569 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-df9c2cf283f048d3b96b6a1a64676d5c2025-08-01T07:25:51ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692025-05-01363G553353910.5802/crmath.73710.5802/crmath.737Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equationAlcantara, Claudemir0Pimentel, Edgard1Urbano, José Miguel2Department of Mathematics, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), 22451-900 Rio de Janeiro, BrazilCMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, PortugalApplied Mathematics and Computational Sciences Program (AMCS), Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955 -6900, Kingdom of Saudi Arabia; CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, PortugalWe examine a semi-linear variant of the bi-Laplacian equation in the superlinear, subquadratic setting and obtain $C^{2,\sigma }$-regularity estimates, depending on the growth regime of the nonlinearity. Our strategy is to render this fourth-order problem as a system of two Poisson equations and explore the interplay between the integrability and smoothness available for each equation taken isolated.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.737/Bi-Laplacian operatorsemi-linear equationsHessian regularityHölder spaces |
| spellingShingle | Alcantara, Claudemir Pimentel, Edgard Urbano, José Miguel Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation Comptes Rendus. Mathématique Bi-Laplacian operator semi-linear equations Hessian regularity Hölder spaces |
| title | Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation |
| title_full | Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation |
| title_fullStr | Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation |
| title_full_unstemmed | Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation |
| title_short | Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation |
| title_sort | hessian regularity in holder spaces for a semi linear bi laplacian equation |
| topic | Bi-Laplacian operator semi-linear equations Hessian regularity Hölder spaces |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.737/ |
| work_keys_str_mv | AT alcantaraclaudemir hessianregularityinholderspacesforasemilinearbilaplacianequation AT pimenteledgard hessianregularityinholderspacesforasemilinearbilaplacianequation AT urbanojosemiguel hessianregularityinholderspacesforasemilinearbilaplacianequation |