We prove an ε-regularity result for a wide class of parabolic systems ut− div(|∇u|p−2∇u|) = B(•, u,∇u|))with the right hand side B growing critically, like | ∇ u|p. 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. Rivière and the last named author.
A conditional regularity result for p-harmonic flows / Kazaniecki, Krystian; Łasica, Michał; Mazowiecka, Katarzyna Ewa; Strzelecki, Paweł. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 23:2(2016). [10.1007/s00030-016-0369-y]
A conditional regularity result for p-harmonic flows
Łasica, Michał;
2016
Abstract
We prove an ε-regularity result for a wide class of parabolic systems ut− div(|∇u|p−2∇u|) = B(•, u,∇u|))with the right hand side B growing critically, like | ∇ u|p. 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. Rivière and the last named author.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
