A conditional regularity result for p-harmonic flows

作者：Kazaniecki Krystian; Lasica Michal; Mazowiecka Katarzyna Ewa; Strzelecki Pawel

来源：Nodea-Nonlinear Differential Equations and Applications, 2016, 23(2): UNSP 9.

DOI：10.1007/s00030-016-0369-y

We prove an epsilon-regularity result for a wide class of parabolic systems
u(t) - div(vertical bar del u vertical bar(p-2)u) = B(center dot, u, u)
with the right hand side B growing critically, like 1Vur. It is assumed a priori that the solution u(t,.) is uniformly small in the space of functions of bounded mean oscillation. The crucial tool is provided by a sharp nonlinear version of the Gagliardo Nirenberg inequality which has been used earlier in the elliptic context by T. Riviere and the last named author.

• 出版日期2016-4