Probablistic Analysis of Semilinear Partial Differential Equation.

1986 ◽  
Author(s):  
Joseph Glover ◽  
Kai L. Chung
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Semilinear Partial Differential Equation

scholarly journals Uniqueness and radial symmetry for an inverse elliptic equation

2003 ◽  
Vol 2003 (48) ◽  
pp. 3047-3052
Author(s):  
B. Emamizadeh ◽  
M. H. Mehrabi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Principle ◽  
Elliptic Equation ◽  
Steady Flow ◽  
Radial Symmetry ◽  
Energy Solution ◽  
Partial Differential ◽  
Dimensional Ball ◽  
Semilinear Partial Differential Equation

We consider an inverse rearrangement semilinear partial differential equation in a 2-dimensional ball and show that it has a unique maximizing energy solution. The solution represents a confined steady flow containing a vortex and passing over a seamount. Our approach is based on a rearrangement variational principle extensively developed by G. R. Burton.

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