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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the Wiener criterion and quasilinear obstacle problems

Authors: Juha Heinonen and Tero Kilpeläinen
Journal: Trans. Amer. Math. Soc. 310 (1988), 239-255
MSC: Primary 35J85; Secondary 49A29
MathSciNet review: 965751
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Abstract: We study the Wiener criterion and variational inequalities with irregular obstacles for quasilinear elliptic operators $ A$, $ A(x,\,\nabla u) \cdot \nabla u \approx \vert\nabla u{\vert^p}$, in $ {{\mathbf{R}}^n}$. Local solutions are continuous at Wiener points of the obstacle function; if $ p > n - 1$, the converse is also shown to be true.

If $ p > n - 1$, then a characterization of the thinness of a set at a point is given in terms of $ A$-superharmonic functions.

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Keywords: Wiener criterion, obstacle problem, $ A$-superharmonic functions
Article copyright: © Copyright 1988 American Mathematical Society