On the Wiener criterion and quasilinear obstacle problems
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- by Juha Heinonen and Tero Kilpeläinen PDF
- Trans. Amer. Math. Soc. 310 (1988), 239-255 Request permission
Abstract:
We study the Wiener criterion and variational inequalities with irregular obstacles for quasilinear elliptic operators $A$, $A(x, \nabla u) \cdot \nabla u \approx |\nabla u{|^p}$, 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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 310 (1988), 239-255
- MSC: Primary 35J85; Secondary 49A29
- DOI: https://doi.org/10.1090/S0002-9947-1988-0965751-8
- MathSciNet review: 965751