Erratum to: Boundary regularity for the supercritical Lane-Emden heat flow

  • Simon Blatt
  • Michael Struwe
Publisher's Erratum

1 Erratum to: Calc. Var. DOI 10.1007/s00526-015-0865-7

The original version of this article unfortunately contained a typographical mistake. The correct statement of Proposition 3.2 is as follows:

Proposition 3.2

There are constants \(C=C(\Omega )\), \(R_{0}=R_{0}(\Omega )>0\) such that for any smooth solution u of (1.1) on \(\Omega \times [0,T[,\) any \(\rho >0\), any \(x_{0} \in \bar{\Omega }\), and any \(0<2r<R_{1}\le \mathrm{min} \{{{R_0},\sqrt{2} \rho ,\sqrt{T/2}}\},\) letting \(t_{0}=T-r^{2}\) with \(\varphi =\varphi ^{\rho }\) there holds
$$\begin{aligned}&\Vert \nabla u\Vert ^2_{L^{2, \mu }(Q_{r}(x_0,t_0))} + \Vert u\Vert ^p_{L^{p, \mu }(Q_{r}(x_0,t_0))}\\&\quad \le C \mathop {\sup }\limits _{\left| {{x_1} - {x_0}} \right| < r} H_{({x_1},T)}^\varphi ({R_1}) + C{R_1} \mathop {\sup }\limits _{{x_1} \in \Omega } H_{({x_1},T)}^\varphi ({R_{1}}) + {C_0}\delta (\rho ,{R_{1}}) \end{aligned}$$
where \({Q_r}({x_0},{t_0}) = {{P} _r}({x_0},{t_0}) \cap \Omega \times [0, T[\).

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität SalzburgSalzburgAustria
  2. 2.Department MathematikETH-ZürichZürichSwitzerland

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