Differential and Integral Equations

Limiting behavior of solutions to an equation with the fractional Laplacian

Xiaoli Chen and Jianfu Yang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we investigate the limiting behavior of solutions $u_p$ of the following subcritical problem \begin{equation}\label{eq:0.1} (-\Delta)^{\frac \alpha 2} u = |x|^\beta u ^ {p-1},\quad u > 0, \quad x\in\Omega ;\quad u = 0,\quad x \in \partial \Omega \end{equation} as $p$ tending to the critical exponent $2^{*}_{\alpha}$, where $\Omega$ is the unit ball in $\mathbb{R}^n$ centered at the origin, and $\beta>0,0 <\alpha <2,\ 2 < p <2^{*}_{\alpha}=\frac{2N}{N-\alpha}$. We show that $u_p$ concentrates on a point on the boundary of the domain as $p\to 2^{*}_{\alpha}$.

Article information

Source
Differential Integral Equations, Volume 27, Number 1/2 (2014), 157-179.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1384282858

Mathematical Reviews number (MathSciNet)
MR3161600

Zentralblatt MATH identifier
1313.35084

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 35B45: A priori estimates 35J70: Degenerate elliptic equations

Citation

Chen, Xiaoli; Yang, Jianfu. Limiting behavior of solutions to an equation with the fractional Laplacian. Differential Integral Equations 27 (2014), no. 1/2, 157--179. https://projecteuclid.org/euclid.die/1384282858


Export citation