Linear and quasilinear parabolic equations in Sobolev space
We consider linear parabolic equations of second order in a Sobolev space setting. We obtain existence and uniqueness results for such equations on a closed two-dimensional manifold, with minimal assumptions about the regularity of the coefficients of the elliptic operator. In particular, we derive a priori estimates relating the Sobolev regularity of the coefficients of the elliptic operator to that of the solution. The results obtained are used in conjunction with an iteration argument to...[Show more]
|Collections||ANU Research Publications|
|Source:||Journal of Differential Equations|
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.