A Spectral Mortar Element Discretization of the Poisson Equation with Mixed Boundary Conditions

2006 ◽  
Vol 30 (2) ◽  
pp. 275-299 ◽  
Author(s):  
Zakaria Belhachmi ◽  
Andreas Karageorghis
Keyword(s):  
Boundary Conditions ◽  
Poisson Equation ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Element Discretization ◽  
The Poisson Equation ◽  
Mortar Element

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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