Work

Local $ L^\infty $ norm estimates for the gradient solutions of variational inequalities arising from the mortgage problems

Year: 2025

Type: article

Abstract: This paper investigates local estimates for the spatial gradient of solutions to variational inequalities within the framework of a parabolic Kirchhoff operator, which arises from mortgage problems. By utilizing the integral inequality for the gradient of the solutions derived in this study, together with the Caffarelli–Kohn–Nirenberg inequality, we establish an $ L^\infty $ norm estimate for the gradient of the solution in a local cylindrical region. This $ L^\infty $ estimate is formulated in terms of the $ L^p $ norm of the solution.

Source: AIMS Mathematics

DOI: 10.3934/math.2025673

Author: Qingjun Zhao

Institution: Chongqing Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W4411793485