Symmetry Results for Classical Solutions of Monge-ampere System in the Plane
نویسندگان
چکیده
In this paper, by the method of moving planes, we prove the symmetry result which says that classical solutions of Monge-Ampere system in the whole plane are symmetric about some point. Our system under consideration comes from the differential geometry problem. Keyword: Moving plane, positive solutions, radial symmetric, MongeAmpere system Mathematics Subject Classification: 35J60, 53C21, 58J05
منابع مشابه
Symmetrically reduced Galileon equations and solutions
The maximally complicated arbitrary-dimensional “maximal” Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D− to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, b...
متن کاملExistence and multiplicity of positive solutions for singular Monge-Amp$rmgrave{e}$re system
Using the fixed point theorem in a cone, the existence and multiplicity of radial convex solutions of singular system of Monge-Amp`{e}re equations are established.
متن کاملA Monge-Ampere Equation with an Unusual Boundary Condition
We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.
متن کاملSubgroup Structure of the Poincaré Group P(1,4) and Symmetry Reduction of Five-Dimensional Equations of Mathematical Physics
Using the subgroup structure of the generalized Poincaré group P (1, 4), the symmetry reduction of the five-dimensional wave and Dirac equations and Euler–Lagrange– Born–Infeld, multidimensional Monge–Ampere, eikonal equations to differential equations with a smaller number of independent variables is done. Some classes of exact solutions of the investigated equations are constructed.
متن کاملPointwise C Estimates at the Boundary for the Monge-ampere Equation
We prove a localization property of boundary sections for solutions to the Monge-Ampere equation. As a consequence we obtain pointwise C2,α estimates at boundary points under appropriate local conditions on the right hand side and boundary data.
متن کامل