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Linear and quasilinear parabolic equations in Sobolev space

Sharples, Jade


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]

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
Source: Journal of Differential Equations
DOI: 10.1016/j.jde.2004.03.020


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