On the weak continuity of elliptic operators and applications to potential theory

Neil S. Trudinger*, Xu Jia Wang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    144 Citations (Scopus)

    Abstract

    In this paper, we establish weak continuity results for quasilinear elliptic and subelliptic operators of divergence form, acting on corresponding classes of subharmonic functions. These results are analogous to our earlier results for fully nonlinear k-Hessian operators. From the weak continuity, we derive various potential theoretic results including capacity estimates, potential estimates and the Wiener criterion for regular boundary points. Our methods make substantial use of Harnack inequalities for solutions.

    Original languageEnglish
    Pages (from-to)369-410
    Number of pages42
    JournalAmerican Journal of Mathematics
    Volume124
    Issue number2
    DOIs
    Publication statusPublished - 2002

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