Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

Free boundary problem for an optimal investment problem with a borrowing constraint

“…A partial differential equation implicitly specifies the solution to the free boundary problem, and the free boundary is determined by the domain over which the PDE must be solved. Due to its analytical intractability resulting from an additional time variable in the associated HJB equation, we turn to investigate the regularity of the solution to associated PDE and the properties of free boundary using techniques derived from theories in the field of differential equations (See eg., Friedman [5,6], Gilbarg and Trudinger [7], Guan, Yi and Chen [10], Lieberman [15]).…”