A Solution to Linear Black-Scholes Second-order Parabolic equation in sobolev space

In this paper, a set of functions were constructed that transforms Black-Scholes partial differential equation into weak formulations. The analytical solutions: existence, uniqueness and other estimates also obtained in form with the use boundary conditions to establish effects its financial implications Sobolev spaces. regularity problem considered which coefficients, domain are all smooth functions. To end, definitions, assumptions paved way useful assertions illustrated paper.