Smoothness improvement for temperatures in terms of the Besov regularity of initial and Dirichlet data
Hugo Aimar, Ivana Gómez · 2012
Jerison and Kenig in J. Funct. Anal. 130 (1995), no.1, 161-219, gave a precise region $\mathcal{R}$ in the square $[0,1]^2$ for the pairs $(s,\tfrac{1}{p})$ for which every harmonic function in the Lipschitz domain $D$, with Dirichlet data in $B^s_p(\partial D)$, belongs to $B^{s+\tfrac{1}{p}}_p(D)$. We prove that every temperature $u$ in $\Omega=D\times (0,T)$ belongs to $\mathbb{B}^{\alpha}_{\tau}(\Omega)$ with $\tfrac{1}{\tau}=\tfrac{1}{p}+\tfrac{\alpha}{d}$, $0