Geodesic
Fine topology and quasilinear elliptic equations
Annales de l'Institut Fourier, Tome 39 (1989) no. 2, pp. 293-318

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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 ( | ∇ u | p - 2 ∇ u ) = 0

continuous. Fine limits of quasiregular and BLD mappings are also studied.

Il est démontré que la topologie fine de type (1,p) définie à l’aide d’un critère de Wiener est la moins fine topologie rendant continues toutes les sursolutions de l’équation p-harmonique

div ( | ∇ u | p - 2 ∇ u ) = 0 .

Les limites fines d’applications quasi-régulières et de type BLD sont aussi étudiées.

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     author = {Heinonen, Juha and Kilpel\"ainen, Terro and Martio, Olli},
     title = {Fine topology and quasilinear elliptic equations},
     journal = {Annales de l'Institut Fourier},
     pages = {293--318},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {39},
     number = {2},
     year = {1989},
     doi = {10.5802/aif.1168},
     mrnumber = {91b:31015},
     zbl = {0659.35038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.1168/}
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Heinonen, Juha; Kilpeläinen, Terro; Martio, Olli. Fine topology and quasilinear elliptic equations. Annales de l'Institut Fourier, Tome 39 (1989) no. 2, pp. 293-318. doi: 10.5802/aif.1168

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