Sobolev Inequalities and Ellipticity of Planar Linear Hamiltonian Systems
نویسندگان
چکیده
In this paper we will establish two different classes of ellipticity criteria, called the L criteria and the L-L criteria respectively, for planar linear Hamiltonian systems with periodic coefficients. The criteria are explicitly expressed using the L and L norms of coefficients and some known Sobolev constants. These results can be considered as the extensions of the famous Lyapunov stability criterion for Hill’s equations. 2000 Mathematics Subject Classification. Primary: 34L40; Secondary: 34L15, 34D20, 93D05.
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