I.7. Symmetry of Solutions – Moving Plane Method

2014 ◽  
pp. 429-468
Author(s):  
Filomena Pacella
Keyword(s):  
Moving Plane Method ◽  
Plane Method ◽  
Moving Plane

A Note on Symmetry of Solutions for a Class of Singular Semilinear Elliptic Problems

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Alessandro Trombetta
Keyword(s):  
Elliptic Equation ◽  
Dirichlet Boundary ◽  
Semilinear Elliptic Equation ◽  
Dirichlet Boundary Conditions ◽  
Moving Plane Method ◽  
Plane Method ◽  
Semilinear Elliptic ◽  
Moving Plane ◽  
Semilinear Elliptic Problems ◽  
Bounded Smooth

AbstractWe prove symmetry and monotonicity properties for positive solutions of the singular semilinear elliptic equationin bounded smooth domains with zero Dirichlet boundary conditions. The well-known moving plane method is applied.

Symmetry of solutions to optimization problems related to partial differential equations

2006 ◽  
Vol 136 (5) ◽  
pp. 921-934 ◽  
Author(s):  
Fabrizio Cuccu ◽  
Giovanni Porru
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Optimization Problems ◽  
Existence Results ◽  
Dirichlet Problems ◽  
Partial Differential ◽  
Moving Plane Method ◽  
Plane Method ◽  
Moving Plane

We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving-plane method to find symmetry results for solutions of a system. We apply these results in our discussion of symmetry for the maximal configurations of the previous problem.

scholarly journals Symmetry of Ground States of p -Laplace Equations via the Moving Plane Method

1999 ◽  
Vol 148 (4) ◽  
pp. 291-308 ◽  
Author(s):  
Lucio Damascelli ◽  
Filomena Pacella ◽  
Mythily Ramaswamy
Keyword(s):  
Ground States ◽  
Moving Plane Method ◽  
Plane Method ◽  
Laplace Equations ◽  
Moving Plane

scholarly journals On the moving plane method for nonlocal problems in bounded domains

2018 ◽  
Vol 135 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Begoña Barrios ◽  
Luigi Montoro ◽  
Berardino Sciunzi
Keyword(s):  
Bounded Domains ◽  
Nonlocal Problems ◽  
Moving Plane Method ◽  
Plane Method ◽  
Moving Plane

scholarly journals The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Francesco Esposito ◽  
Berardino Sciunzi
Keyword(s):  
Elliptic Equations ◽  
Order Term ◽  
Singular Solutions ◽  
Moving Plane Method ◽  
Plane Method ◽  
First Order ◽  
Semilinear Elliptic ◽  
Singular Elliptic Equations ◽  
Moving Plane ◽  
Semilinear Elliptic Problems

Abstract In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.

scholarly journals The moving plane method for singular semilinear elliptic problems

2017 ◽  
Vol 156 ◽  
pp. 61-69 ◽  
Author(s):  
Annamaria Canino ◽  
Luigi Montoro ◽  
Berardino Sciunzi
Keyword(s):  
Elliptic Problems ◽  
Moving Plane Method ◽  
Plane Method ◽  
Semilinear Elliptic ◽  
Moving Plane ◽  
Semilinear Elliptic Problems
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