Equations of the form du = (auxx + fx) dt + Σk(σkux + gk) dwtk are considered for t > 0 and x > 0. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power p ∈ [2, ∞).
|Original language||English (US)|
|Number of pages||28|
|Journal||SIAM Journal on Mathematical Analysis|
|State||Published - 1998|
- Sobolev spaces with weights
- Stochastic partial differential equations