scholarly journals Existence and uniqueness of viscosity solutions to the exterior problem of a parabolic Monge-Ampère equation

2020 ◽  
Vol 19 (10) ◽  
pp. 4921-4936
Author(s):  
Shuyu Gong ◽  
◽  
Ziwei Zhou ◽  
Jiguang Bao
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Exterior Problem ◽  
Monge Ampere

Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

2020 ◽  
Vol 20 (4) ◽  
pp. 769-781
Author(s):  
Limei Dai ◽  
Jiguang Bao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Entire Solutions ◽  
Perron Method ◽  
The Cauchy Problem ◽  
Monge Ampere

AbstractIn this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation-u_{t}\det D^{2}u=f(x,t)and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

scholarly journals Time Remotely Almost Periodic Viscosity Solutions of Hamilton-Jacobi Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shilin Zhang ◽  
Daxiong Piao
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Functions ◽  
Periodic Case ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Jacobi Equations

We study some properties of the remotely almost periodic functions. This paper studies viscosity solutions of general Hamilton-Jacobi equations in the time remotely almost periodic case. Existence and uniqueness results are presented under usual hypotheses.

scholarly journals Viscosity solutions to quaternionic Monge–Ampère equations

2016 ◽  
Vol 140 ◽  
pp. 69-81 ◽  
Author(s):  
Dongrui Wan ◽  
Wei Wang
Keyword(s):  
Viscosity Solutions ◽  
Monge Ampere

scholarly journals DEGENERATE COMPLEX MONGE–AMPÈRE EQUATIONS OVER COMPACT KÄHLER MANIFOLDS

2010 ◽  
Vol 21 (03) ◽  
pp. 357-405 ◽  
Author(s):  
JEAN-PIERRE DEMAILLY ◽  
NEFTON PALI
Keyword(s):  
Existence And Uniqueness ◽  
General Type ◽  
Einstein Metrics ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Canonical Sheaf ◽  
Kähler Einstein Metrics ◽  
Monge Ampere

We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge–Ampère equations, and investigate their regularity. These types of equations are precisely what is needed in order to construct Kähler–Einstein metrics over irreducible singular Kähler spaces with ample or trivial canonical sheaf and singular Kähler–Einstein metrics over varieties of general type.

scholarly journals Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians

2019 ◽  
Vol 21 (01) ◽  
pp. 1750098 ◽  
Author(s):  
Andrea Davini
Keyword(s):  
Viscosity Solution ◽  
Viscosity Solutions ◽  
Parabolic Equations ◽  
General Class ◽  
Existence And Uniqueness ◽  
Quasilinear Equations ◽  
Uniqueness Of Solutions ◽  
Superlinear Growth ◽  
Lipschitz Estimates ◽  
Jacobi Equations

We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the gradient variable. The approach is mainly based on classical techniques for uniformly parabolic quasilinear equations and on the Lipschitz estimates provided in [S. N. Armstrong and H. V. Tran, Viscosity solutions of general viscous Hamilton–Jacobi equations, Math. Ann. 361 (2015) 647–687], as well as on viscosity solution arguments.

scholarly journals Viscosity solutions of the Monge–Ampère equation with the right hand side in Lp

2007 ◽  
pp. 221-233
Author(s):  
Barbara Brandolini ◽  
Cristina Trombetti ◽  
Anna Lisa Amadori
Keyword(s):  
Viscosity Solutions ◽  
Right Hand ◽  
The Right ◽  
Monge Ampere

scholarly journals Pluripotential solutions versus viscosity solutions to complex Monge–Ampère flows

2021 ◽  
Vol 17 (3) ◽  
pp. 971-990
Author(s):  
Vincent Guedj ◽  
Chinh H. Lu ◽  
Ahmed Zeriahi
Keyword(s):  
Viscosity Solutions ◽  
Monge Ampere

scholarly journals A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics

2017 ◽  
Vol 2019 (17) ◽  
pp. 5497-5538 ◽  
Author(s):  
Tao Zheng
Keyword(s):  
Smooth Function ◽  
Existence And Uniqueness ◽  
Type Equation ◽  
Uniqueness Of Solution ◽  
Long Time Existence ◽  
Hermitian Manifolds ◽  
Long Time ◽  
Monge Ampere ◽  
Time Existence

Abstract We prove the long time existence and uniqueness of solution to a parabolic Monge–Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the solution converges to a smooth function in the smooth topology as $t$ approaches infinity which, up to scaling, is the solution to a Monge–Ampère type equation. This gives a parabolic proof of the Gauduchon conjecture based on the solution of Székelyhidi, Tosatti, and Weinkove to this conjecture.

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