Explicit Estimates on the Fundamental Solution of Higher-Order Parabolic Equations with Measurable Coefficients

Sharp Heat-Kernel Estimates for Higher-Order Operators With Singular Coefficients

“…In the special case where H is uniformly elliptic and self-adjoint this estimate has already been obtained in [4]. …”

Gaussian estimates with best constants for higher-order Schrödinger operators with Kato potentials

“…The purpose of the present note is to show that if 2m > n then more can be achieved by an adaptation of the methods of [6]. Using purely L 2 methods we obtain a sharp Gaussian estimate for the heat kernel of H 0 + V for operators H 0 with variable coefficients.…”

On the heat kernel of a class of fourth order operators in two dimensions: Sharp Gaussian estimates and short time asymptotics

“…For the proof one simply uses the relation D α u(x) = (2π) −1 R 2 (iξ) α e ix·ξû (ξ)dξ for the various terms that appear in Q 1,λϕ . Since a very similar proof has been given in [2] we omit further details (the fact that k(x) is not constant in our case is not a problem and strong convexity is not relevant here).…”

“…We note however that in [2] (where the coefficients α, β, γ are functions) the term strong convexity was also used for the slightly more general situation where…”