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Fine topology and quasilinear elliptic equations

Juha Heinonen; Terro Kilpeläinen; Olli Martio — 1989

Annales de l'institut Fourier

It is shown that the $(1, p)$ -fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the $p$ -Laplace equation $div (| \nabla u |^{p - 2} \nabla u) = 0$ continuous. Fine limits of quasiregular and BLD mappings are also studied.

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