Weak Solution of Parabolic Complex Monge-ampère Equation
نویسنده
چکیده
We study the equation u̇ = log det(uαβ̄)−Au+f(z, t) in domains of C. This equation has a close connection with the Kähler-Ricci flow. In this paper, we consider the case where the boundary condition is smooth and the initial condition is irregular.
منابع مشابه
ON A PRIORI C1,α AND W2,p ESTIMATES FOR A PARABOLIC MONGE-AMPÈRE EQUATION IN THE GAUSS CURVATURE FLOWS
This paper establishes Hölder estimates of Du and Lp estimates of D2u for solutions u to the parabolic Monge-Ampère equation −Aut + ( det D2u)1/n = f .
متن کاملThe General Solution of the Complex Monge-Ampère Equation in a space of arbitrary dimension
A general solution to the Complex Monge-Ampère equation in a space of arbitrary dimensions is constructed.
متن کاملThe General Solution of the Complex Monge-Ampère Equation in two dimensional space
The general solution to the Complex Monge-Ampère equation in a two dimensional space is constructed.
متن کاملNormal forms for parabolic Monge-Ampère equations
We find normal forms for parabolic Monge-Ampère equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case, this equation is shown to have solutions. The other normal forms exhaust the different classes of parabolic Monge-Ampère equations with symmetry p...
متن کاملHarnack Inequality for Time-dependent Linearized Parabolic Monge-ampère Equation
We prove a Harnack inequality for nonnegative solutions of linearized parabolic Monge-Ampère equations −t φt − tr((Dφ)Du) = 0, in terms of a variant of parabolic sections associated with φ, where φ satisfies λ ≤ −φt detDφ ≤ Λ and C1 ≤ −φt ≤ C2.
متن کامل