2017/02/15 by Katharina Brazda, Maarten V. de Hoop, Brazda, Katharina +3
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #49S05 #86-02 #Action (physics) #Calculus of variations #Classical mechanics #Differentiable function #Earth (classical element) #Euler equations #FOS: Physical sciences #Geophysics and Gravity Measurements #Gravitation #High-pressure geophysics and materials #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Sobolev space #earthquake and tectonic studies #math-ph #math.MP #msc:49S05 #msc:86-02
paper · pdf · doi:10.48550/arxiv.1702.04741
1 figure
arxiv created 2017/02/15 · openalex publication_date 2017/02/15 · arxiv updated 2017/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a construction of the action, in the framework of the calculus of variations and Sobolev spaces, describing deformations and the oscillations of a uniformly rotating, elastic and self-gravitating earth. We establish the Fréchet differentiability of the action under minimal regularity assumptions, which constrain the possible composition of an earth model. Thus we obtain well-defined Euler-Lagrange equations, weakly and strongly, that is, the system of elastic-gravitational equations.