Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
We establish higher-order weighted Sobolev and Hölder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance [27]. Furthermore, given $C^\infty$-smooth data, we prove $C^\infty$-regularity of solutions up to the portion of the boundary where the operator is degenerate. …