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Abstract

A Cauchy-Liouville type theorem is a statement that under appropriate circumstances an entire solution (a solution defined over ℝn) of an elliptic equation must be constant.1 For the Laplace equation in particular, it is enough that a solution u should be bounded, or even, at a minimum, that u(x) = o(|x|) as |x| → ∞. For quasilinear equations, and even for semilinear equations of the form Δu + B(u, Du) = 0, x ∈ ℝn, (8.1.1) the same question is more delicate than might at first be expected, since a number of different kinds of behavior can be seen even for relatively simple examples.

Keywords

Riemannian Manifold Lipschitz Continuity Exterior Domain Entire Solution Distribution Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2007

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