Work

Higher order Schauder estimates for degenerate or singular parabolic equations

Year: 2025

Type: article

Abstract: In this paper, we complete the analysis initiated in [Calc. Var. Partial Differential Equations 63 (2024), article no. 204] establishing some higher order C^{k+2,\alpha} Schauder estimates ( k \in \mathbb{N} ) for a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The C^{2,\alpha} -estimates are obtained through a blow-up argument and a Liouville theorem, while the higher order estimates are obtained by a fine iteration procedure. As a byproduct, we present two applications. First, we prove similar Schauder estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type. Second, we provide an alternative proof of the higher order boundary Harnack principles established in [J. Differential Equations 260 (2016), 1801–1829] and [Discrete Contin. Dyn. Syst. 42 (2022), 2667–2698].

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1540

Authors: Alessandro Audrito, Gabriele Fioravanti, Stefano Vita

Institutions: Politecnico di Torino, University of Turin, University of Pavia

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Istituto Nazionale di Alta Matematica "Francesco Severi"

Awards: G5339074417, G5456286744