scholarly journals Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains

2011 ◽  
Vol 1 (1) ◽  
pp. 33-77 ◽  
Author(s):  
Vladimir Maz’ya ◽  
Tatyana Shaposhnikova
Keyword(s):  
Elliptic Equations ◽  
Recent Progress ◽  
Arbitrary Order ◽  
Lipschitz Domains ◽  
Rough Coefficients

scholarly journals THE INITIAL VALUE PROBLEM IN NUMERICAL RELATIVITY

2005 ◽  
Vol 02 (02) ◽  
pp. 497-520 ◽  
Author(s):  
HARALD P. PFEIFFER
Keyword(s):  
Black Hole ◽  
Initial Data ◽  
Initial Value Problem ◽  
Elliptic Equations ◽  
Recent Progress ◽  
Extrinsic Curvature ◽  
Numerical Techniques ◽  
Initial Value ◽  
Binary Black Hole ◽  
Conformal Method

The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages due to the recent introduction of a weight-function in the extrinsic curvature decomposition are discussed. I then describe recent progress in numerical techniques to solve the resulting elliptic equations, and explore innovative approaches toward the construction of astrophysically realistic initial data for binary black hole simulations.

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