Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
Abstract
In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove Lp - Lq estimates for the solutions of the equation with and without a source term.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- January 2009
- DOI:
- 10.1007/s00220-008-0649-4
- arXiv:
- arXiv:0803.3074
- Bibcode:
- 2009CMaPh.285..293Y
- Keywords:
-
- Black Hole;
- Wave Equation;
- Cauchy Problem;
- Source Term;
- Fundamental Solution;
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- 35C15;
- 35L05;
- 35Q75;
- 35L15
- E-Print:
- Comm. Math. Phys., 285 (2009), 293-344.