Generation of Analytic Semigroups by Elliptic Operators with Unbounded Coefficients
Piermarco Cannarsa, Vincenzo Vesprı · SIAM Journal on Mathematical Analysis · 1987
Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate analytic semigroups of linear operators on $L^2 (R^N )$, $L^{2,\mu } (R^N )$, $C(R^N )$ and $C^\alpha (R^N )$. Some of these generation results are applied to parabolic initial value problems.