Work

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

Year: 2026

Type: article

Abstract: We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required.

Source: Annali di Matematica Pura ed Applicata (1923 -)

DOI: 10.1007/s10231-026-01672-6

Authors: Giuseppe Spadaro, Domenico Vuono

Institution: University of Calabria

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università della Calabria