Answer by Ayman Moussa for Different ways to prove $L^p$-estimates for the...
In the book "Second Order Parabolic Differential Equations" of G. M. Lieberman, such estimates are recovered (see Chapter VII) on a domain $\Omega$ with adequate boundary conditions. He introduces a...
View ArticleAnswer by Giorgio Metafune for Different ways to prove $L^p$-estimates for...
I would say that methods 1) and 2) are very close each other but in both cases the proof is a bit harder than the elliptic counterpart since one has to use the Marcinkiewicz multiplier theorem instead...
View ArticleDifferent ways to prove $L^p$-estimates for the heat equation
Let $p \in (1,\infty)$. We are interested in strong $L^p$-solutions to the heat equation in $\mathbb{R}^n$.$$\begin{cases} \partial_t u = \Delta u + f \\u(0) = 0.\end{cases}$$It is well-known that for...
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