Fourth-order Schrödinger operators with potentials growing slower than |x|^4 are quasi-sectorial on Lp(R^N) for 1<p<∞, generate analytic semigroups, and have domain equal to the intersection of the domains of the fourth-order operator and the multiplication operator.
Lunardi,Analytic semigroups and optimal regularity in parabolic problems, Birkhauser
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Higher order Schr\"odinger operators
Fourth-order Schrödinger operators with potentials growing slower than |x|^4 are quasi-sectorial on Lp(R^N) for 1<p<∞, generate analytic semigroups, and have domain equal to the intersection of the domains of the fourth-order operator and the multiplication operator.