Interpolation of nonlinear partial differential operators and generation of differentiale evolutions

Sharp convergence rates for nonlinear product formulas

“…The class of operators considered in this paper is slightly more complicated and less general than the class of "»»-generators" studied in [15], [16]. In Section 6 we shall show that the generators of the present paper are a subclass of the »'-generators.…”

“…The arguments of this paper can be made to work with slightly weaker hypotheses on \p and w; see [15], [16] for similar arguments. But that would require longer definitions and proofs, so for brevity we shall use the conditions on \p and w indicated above.…”

“…A version of (0.1) was proved for »»-generators in [16], but the convergence rate was not optimal. To prove the optimal rate (0.3), we need hypotheses a bit stronger than those of [15], [16]. This paper, and several other related papers, grew out of a portion of the author's Ph.D thesis, which was written at the University of Chicago under the supervision of Jerry Bona.…”

“…The function w plays a role analogous to the constant w which appears in much of the literature on nonlinear semigroup theory [2], [3], [5], [6]. But a constant will not suffice for some applications; see the examples in [14], [15].…”

“…It is not clear whether this qualitative condition can be replaced with a quantitative one. Property 1.3(a) is discussed further in [15].…”