In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by [formula] on smooth domain and for varying nonlinearity ∫.
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We investigate conditional stable processes in a Lipschitz domain D and conditional stable processes in the image of D under the Kelvin transform. We show that, with a suitable change of time, these processes are equal in distribution. As an application, we show the equivalence of the Hardy spaces and the relative Fatou theorem for D and its image.
Our aim is to get characterizations and unconditional bases of variable Sobolev spaces Lp (·),s(Rn) in terms of wavelets. As an application, we obtain the sampling theorem in Lp (·),s(Rn).
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