Abstract
In this paper, we use the moving planes method to prove that the domain Ω and the solution u are Steiner symmetric if u is a positive solution of the overdetermined boundary value problem in Ω.
Highlights
We will present some symmetry results in overdetermined boundary value problem u f x,u, u 0 in u 0 on u c x onFor the motion of a viscous incompressible fluid moving in straight parallel streamlines through a pipe with planar section or the torsion of a solid straight bar of given cross section, both of them can be described by the following overdetermined problem u 1 in u 0 on problem has a solution u in C2, must be a ball
We use the moving planes method to prove that the domain Ω and the solution u are Steiner symmetric if u is a positive solution of the overdetermined boundary value problem in Ω
We will introduce the notations in the moving planes method and four results
Summary
We use the moving planes method to prove that the domain Ω and the solution u are Steiner symmetric if u is a positive solution of the overdetermined boundary value problem in Ω. We will present some symmetry results in overdetermined boundary value problem U const on where is a bounded domain of class C2 in Rn such that there exists a function u satisfying the above problem, and is the unit normal to .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
