Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation (Preprint)

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Type: Preprint
National /International: International
Title: Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation
Publication Date: 2024-03-28
Authors: - Claudemir Alcantara
- Edgard Almeida Pimentel
- José Miguel Urbano
Abstract:

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.

Institution: DMUC 24-19
Online version: http://www.mat.uc.pt...prints/eng_2024.html
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