On some degenerate parabolic equations

Abstract

Let Ω, I be open intervals in Rx = (— ∞ < x < ∞), Rt = (— ∞ < t < ∞) respectively. For a function a(x, t) ∈ C∞(Ω × I), consider the partial differential operator(1.1) .

On some degenerate parabolic equations II

“…As in [8], we can show that (iv) the second term in the right of (i) is also very regular and becomes smoother in R x x R y x / x I according as μ becomes larger.…”

“…Introduction. In the article I: [8], we have proved the hypoellipticity of a degenerate parabolic equation of the form:…”

“…As in [8], we have the following proposition: For the notations in the proposition we refer to the article [8].…”

Hypoelliptic Degenerate Evolution Equations of the Second Order

“…The above proposition and remark imply Proposition 2.1 by the same way as T. Matsuzawa [8]. In fact, let us prove it assuming Proposition 3.1, and Proposition 3.1 will be proved in the following sections.…”

“…§2 8 An Outline of the Proof of Theorem As mentioned in section I, we shall prove only Theorem-(i), so we assume that 1 0 is a non-negative even integer.…”