Hölder and Schauder estimates for weak solutions of a certain class of non-divergent variation inequality problems in finance

Abstract

This article studies a class of variational inequality problems composed of non-divergence type parabolic operators. In comparison with traditional differential equations, this study focuses on overcoming inequality constraints to obtain Hölder and Schauder estimates for weak solutions. The results indicate that the weak solution of the variational inequality possesses the $ C^ \alpha $ continuity and the Schauder estimate on the $ W^{1, p} $ space, where $ \alpha \in (0, 1) $ and $ p\geq 2 $.

Keywords

• variation-inequality problems
• non-divergence type parabolic operator
• hölder and schauder estimate