Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential

Abstract

Abstract. Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations

Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential

“…To prove estimate (1.14) in Theorem 1.3, we apply the following comparison principle established in [12] (see [12,Theorem 3.2]).…”

“…where h is a bounded function. The proof of Proposition 3.1 is the same as that of Proposition 2.1 of [12], with minor modifications. We omit the details.…”

Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential

“…In [17], the author obtained the following result on the asymptotic behaviors of solutions to equation (1.1) both at the origin and at the infinity. Theorem 1.1.…”

“…Then the constants C, R 0 , R 1 in Theorem 1.1 and Theorem 1.2 depend also on r 0 . The reader is referred to find more details on this dependence in [17].…”

Caccioppoli-type estimates and Hardy-type inequalities derived from weighted p-harmonic problems

“…Derivation of the Hardy inequalities on the basis of supersolutions to p-harmonic differential problems can be found in papers by D'Ambrosio [22][23][24] and Barbatis et al [5,6]. Other interesting results linking the existence of solutions in elliptic and parabolic PDEs with Hardy type inequalities are presented in [2,4,36,61,62], see also references therein. We refer also to the contribution by the third author [56], where instead of the nonweighted p-Laplacian in (1.1) one deals with the A-Laplacian: A u = div A (|∇u|) |∇u| 2 ∇u , involving a function A from an Orlicz class.…”