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.
|Original language||English (US)|
|Number of pages||25|
|Journal||SIAM Journal on Mathematical Analysis|
|State||Published - 2005|
- C domains
- Parabolic equations
- Sobolev spaces with weights