On the sobolev space theory of parabolic and elliptic equations in C ¹ domains

Existence and uniqueness results are given for second-order parabolic and elliptic equations with variable coefficients in C ¹ domains in Sobolev spaces with weights allowing the derivatives of solutions to blow up near the boundary. The "number" of derivatives can be negative and fractional. The coefficients of parabolic equations are only assumed to be measurable in time.