Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space

@article{Ignat2011LowerAU,
  title={Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space},
  author={L. Ignat and J. Rossi and A. S. Antol{\'i}n},
  journal={Journal of Differential Equations},
  year={2011},
  volume={252},
  pages={6429-6447}
}
Abstract We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T ( u ) = − ∫ R d K ( x , y ) ( u ( y ) − u ( x ) ) d y . Here we consider a kernel K ( x , y ) = ψ ( y − a ( x ) ) + ψ ( x − a ( y ) ) where ψ is a bounded, nonnegative function supported in the unit ball and a means a diffeomorphism on R d . A simple example being a linear function a ( x ) = A x . The upper and lower bounds that we obtain are given in terms of the Jacobian of a and… Expand
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