Nonexistence of distributional supersolutions of a semilinear elliptic equation with Hardy potential

In this paper we study nonexistence of non-negative distributional supersolutions for a class of semilinear elliptic equations involving inverse-square potentials.Comment: Some of the main results are improved. To appear in Journal of Functional Analysi

Unique continuation property and local asymptotics of solutions to fractional elliptic equations

Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the singularity of solutions to linear and semilinear fractional elliptic equations with a homogeneous singular potential related to the fractional Hardy inequality. As a consequence we obtain unique continuation properties for fractional elliptic equations.Comment: This is a revision of arXiv:1301.5119v1: some minor changes have been made and Theorem 1.3 has been adde

Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials

In this paper we deal with nonnegative distributional supersolutions for a class of linear elliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results