On a singular elliptic equation

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Abstract

In this paper, we study the singular elliptic equation Lu + K(x)up = 0. where L is a uniformly elliptic operator of divergence form, p > 1 and K(x) has a singularity at the origin. We prove that this equation does not possess any positive (local) solution in any punctured neighborhood of the origin if there exist two constants C1, C2 such that C1 |x|σ ≥ K(x) ≥ C2 | x |σ near the origin for some σ ≥ -2 (with no other condition on the gradient of K). In fact, an integral condition is derived.

Original languageEnglish (US)
Pages (from-to)614-616
Number of pages3
JournalProceedings of the American Mathematical Society
Volume88
Issue number4
DOIs
StatePublished - Aug 1983

Keywords

  • Nonexistence
  • Singular elliptic equation

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