A Note on the Heat Flow of Harmonic Maps Whose Gradients Belong to (LtLxP)-L-q

作者：Dai, Junfei^*; Luo, Wei; Wang, Meng

来源：Pure and Applied Mathematics Quarterly, 2015, 11(2): 283-292.

DOI：10.4310/PAMQ.2015.v11.n2.a5

• Heat flow
• Suitable solution
• Lorentz space
• Blow up

For any compact n-dimensional Riemannian manifold (M, g) without boundary, a compact Riemannian manifold N subset of R-k without boundary, and 0 < T <= infinity, we prove that for n >= 3, if u : M x (0, T] -> N is a weak solution to the heat flow of harmonic maps such that Delta u is an element of (LxLtq)-L-p(M x (0, T]) (n/p + 2/q = 1 for some p > n), then u is an element of C-infinity(M x (0,T), N). For p = n, we proved the regularity for the suitable weak solution defined in [1].

• 出版日期2015-4
• 单位浙江大学