Geodesic
Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 429-435

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We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $p$-Laplacian type. If $p\gamma $ and the right-hand side is a Radon measure with singularity of order $\gamma $ at $x_0\in \Omega $, then any supersolution in $W_{\mathrm loc}^{1,p}(\Omega )$ has singularity of order at least $\frac{(\gamma -p)}{(p-1)}$ at $x_0$. In the proof we exploit a pointwise estimate of $\mathcal A$-superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.
Classification : 31B05, 35A20, 35B05, 35J60
Keywords: quasilinear elliptic; singularity; Sobolev function 
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     author = {\v{Z}ubrini\'c, Darko},
     title = {Generating singularities of solutions of quasilinear elliptic equations using {Wolff{\textquoteright}s} potential},
     journal = {Czechoslovak Mathematical Journal},
     pages = {429--435},
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     volume = {53},
     number = {2},
     year = {2003},
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     zbl = {1022.31005},
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Žubrinić, Darko. Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 429-435. http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a16/