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Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential. (English) Zbl 1022.31005
Summary: We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $$p$$-Laplacian type. If $$p<\gamma <N$$ and the right-hand side is a Radon measure with singularity of order $$\gamma$$ at $$x_0\in \Omega$$, then any supersolution in $$W_{\text{loc}}^{1,p}(\Omega)$$ has singularity of order at least $$(\gamma -p)/(p-1)$$ at $$x_0$$. In the proof we exploit a pointwise estimate of $$\mathcal A$$-superharmonic solutions, due to T. Kilpeläinen and J. Malý, which involves Wolff’s potential of Radon’s measure.
MSC:
 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 35J60 Nonlinear elliptic equations 35A20 Analyticity in context of PDEs
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References:
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