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

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 ${Q_r}({x_0},{t_0}) = {{P} _r}({x_0},{t_0}) \cap \Omega \times [0, T[$.