Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential

Darko Žubrinić

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 2, page 429-435
  • ISSN: 0011-4642

Abstract

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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 < γ < N and the right-hand side is a Radon measure with singularity of order γ at x 0 ∈ Ω , then any supersolution in W l o c 1 , p ( Ω ) has singularity of order at least ( γ - p ) ( p - 1 ) at x 0 . In the proof we exploit a pointwise estimate of 𝒜 -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.

How to cite

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Žubrinić, Darko. "Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential." Czechoslovak Mathematical Journal 53.2 (2003): 429-435. <http://eudml.org/doc/30788>.

@article{Žubrinić2003,
abstract = {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 $W_\{\mathrm \{l\}oc\}^\{1,p\}(\Omega )$ 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.},
author = {Žubrinić, Darko},
journal = {Czechoslovak Mathematical Journal},
keywords = {quasilinear elliptic; singularity; Sobolev function; -Laplacian; singularity; Radon measure; -superharmonic solutions; Wolff's potential},
language = {eng},
number = {2},
pages = {429-435},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential},
url = {http://eudml.org/doc/30788},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Žubrinić, Darko
TI - Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 429
EP - 435
AB - 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 $W_{\mathrm {l}oc}^{1,p}(\Omega )$ 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.
LA - eng
KW - quasilinear elliptic; singularity; Sobolev function; -Laplacian; singularity; Radon measure; -superharmonic solutions; Wolff's potential
UR - http://eudml.org/doc/30788
ER -

References

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