Criterion for the $L^p$-dissipativity of second order differential operators with complex coefficients

Alberto Cialdea, Vladimir Maz'ya

We prove that the algebraic condition $|p-2||<\mathcal{I}m\mathcal{A}\xi ,\xi >|\le 2\sqrt{p-1}<\mathcal{R}e\mathcal{A}\xi ,\xi >$ (for any $\xi \in {\mathbb{R}}^n$) is necessary and su…