We consider second-order divergence form uniformly parabolic and elliptic PDEs with bounded and VMOx leading coefficients and possibly linearly growing lower-order coefficients. We look for solutions which are summable to the pth power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variables.
|Original language||English (US)|
|Title of host publication||Progress in Nonlinear Differential Equations and Their Application|
|Number of pages||26|
|State||Published - 2011|
|Name||Progress in Nonlinear Differential Equations and Their Application|
Bibliographical noteFunding Information:
The work was partially supported by NSF grant DMS-0653121.
- Divergence type equations
- Growing coefficients
- Sobolev spaces without weights
- Stochastic partial differential equations