The regularity and minimal-growth solution conjecture for Fuchsian singularities

Let Ω^\hat{\Omega} be the one-point compactification of the domain associated with Equation Qp,A,V(u)=0Q_{p,A,V}(u)=0, and let ζΩ^\zeta\in\partial\hat{\Omega}. Assume that ζ\zeta is a Fuchsian-type isolated singularity of the equation and that the equation admits a global positive solution.

Regularity and minimal-growth solution conjecture. Then:

  1. ζ\zeta is a regular point of the equation.
  2. The equation admits a unique global positive solution of minimal growth in a neighborhood of Ω^{ζ}\partial\hat{\Omega}\setminus\{\zeta\}.

The paper presents this as an extension of a conjecture of Frass and Pinchover to the (p,A)(p,A)-Laplacian setting with Fuchsian potentials in Morrey space, and aims to prove it under additional relatively mild assumptions. The supplied text does not establish the conjecture in full.

Sources & referencesView supporting material

Primary source

Ratan Kr. Giri and Yehuda Pinchover, “Positive Liouville theorem and asymptotic behaviour for (p,A)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space”, arXiv:2007.02254 (2020).

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