Abstract
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 yield existence results for quasilinear parabolic equations.
Original language | English |
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Pages (from-to) | 111-142 |
Number of pages | 32 |
Journal | Journal of Differential Equations |
Volume | 202 |
Issue number | 1 |
DOIs | |
Publication status | Published - 15 Jul 2004 |