On optimal derivative estimate for solutions to the heat equation with continuous bounded initial data
Dong-Ho Tsai · International Journal of Mathematics · 2025
In this paper, we study the optimal derivative estimate problem (for [Formula: see text] and for [Formula: see text], respectively) for convolution solutions of the one-dimensional heat equation with initial data lying in the function space [Formula: see text]. We also make certain generalization to the linear equation with constant coefficients.