Local gradient estimation for nonlinear degenerate parabolic variational inequalities derived from the value analysis of financial derivatives

Abstract This study examines the spatial gradient estimation of solutions to a particular class of variational inequality problems that arise from the structure of nonlinear degenerate parabolic operators. Specifically, under the assumption that 2 ≤ p ≤ 2 (1 + 2 n) 2 p 2 (1+2/n. ) (where n denotes the spatial dimension), we derive an estimate for the spatial gradient of the solution within a local cylindrical domain, referred to as the L p energy estimate, which is complemented by an additional L 2 estimate.