Advances in Differential Equations

On partial regularity of the borderline solution of semilinear parabolic equation with critical growth

Shi-Zhong Du

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 consider the borderline solution to the semilinear equations with critical growth. A concentration phenomenon of the solution when the time goes to infinity is proved. First, we show that a $\varepsilon$-regularity property holds for an $H^1$ solution to the related elliptic equation, and then give a precise description of the formation of the bubbles. A similar bubbling description is also derived for the harmonic maps on surface. (Cf.~Struwe [22], Qing [19], Qing-Tian [20], Chen-Tian [6], Lin-Wang [13], and Parker [16]).

Article information

Source
Adv. Differential Equations Volume 18, Number 1/2 (2013), 147-177.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867484

Mathematical Reviews number (MathSciNet)
MR3052713

Zentralblatt MATH identifier
1262.35067

Subjects
Primary: 35K55: Nonlinear parabolic equations 35D10 35B65: Smoothness and regularity of solutions

Citation

Du, Shi-Zhong. On partial regularity of the borderline solution of semilinear parabolic equation with critical growth. Adv. Differential Equations 18 (2013), no. 1/2, 147--177. https://projecteuclid.org/euclid.ade/1355867484.


Export citation