Isolated singularities of nonlinear elliptic inequalities

Abstract

We give conditions on a continuous function f : (0, ∞) → (0, ∞) which guarantee that everyin a punctured neighborhood of the origin in R R R n (n ≥ 2) is asymptotically radial (or asymptotically harmonic) as |x| → 0 + .

Pointwise bounds and blow-up for nonlinear polyharmonic inequalities

“…The following three theorems, which we proved in [8], [16], and [15], completely answer Question 1 when m and n satisfy either (i), (ii), or (iii). Consequently, in this paper, we will only prove results dealing with the case that m and n satisfy either (iv) or (v).…”

On n-superharmonic functions and some geometric applications

“…Our second goal is to eliminate nontrivial n-thin subsets E in Theorem 1.1. This theorem in general dimensions is inspired by and extends the work of Taliaferro in [61][62][63]. induced by a nonnegative function in L 1 ( ), where D is the diameter of and δ ∈ (0, 1).…”

“…As stated in Remark 4.1, the critical growth condition may be described as 0 ≤ f (x, w, ∇w) ≤ C|∇w| p e αw (1.8) for any 0 < p < n and α > 0 to be more general. Our proof of Theorem 1.2 is a streamlined one from [61][62][63] with the help of the Adams-Moser-Trudinger inequality (1.7) for the Wolff potential.…”

Arbitrarily large solutions of the conformal scalar curvature problem at an isolated singularity

“…Finally, Taliaferro [7], [8] has studied arbitrarily large solutions of (1.1) with the exponent n * replaced by a constant λ < n * .…”