A -theory of parabolic equations with unbounded leading coefficients on non-smooth domains

We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hِlder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.