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Properties of solutions to some weighted ρLlaplacian equation

Garain Prashanta

Opuscula Mathematica

2020

Vol. 40, no. 4

483--494

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 ∫.

Kelvin transform for (…)-harmonic functions in regular domains

Michalik K., Ryznar M.

Demonstratio Mathematica

2012

Vol. 45, nr 2

361-376

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.

Wavelet characterization of Sobolev spaces with variable exponent

Izuki M.

Journal of Applied Analysis

2011

Vol. 17, nr 1

37-49

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).