Regularity and higher integrability of weak solutions to a class of non-Newtonian variation-inequality problems arising from American lookback options

Abstract

This paper presents the proofs of the higher integrability and regularity of weak solutions to a class of variation-inequality problems that are formulated by a non-Newtonian parabolic operator. After obtaining the gradient estimate, the higher order integrability of the weak solution is analyzed. We also examine the internal regularity estimate of the weak solution by utilizing a test function of the difference type.

Keywords

• variation-inequality problems
• non-newtonian parabolic operator
• higher integrability
• regularity