Linear and quasilinear parabolic equations in Sobolev space

Jason J. Sharples*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)111-142
    Number of pages32
    JournalJournal of Differential Equations
    Volume202
    Issue number1
    DOIs
    Publication statusPublished - 15 Jul 2004

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