Advances in Differential Equations
- Adv. Differential Equations
- Volume 18, Number 1/2 (2013), 147-177.
On partial regularity of the borderline solution of semilinear parabolic equation with critical growth
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 , Qing , Qing-Tian , Chen-Tian , Lin-Wang , and Parker ).
Adv. Differential Equations, Volume 18, Number 1/2 (2013), 147-177.
First available in Project Euclid: 18 December 2012
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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