Abstract
We study properties of \(\mathcal {A}\)-harmonic and \(\mathcal {A}\)-superharmonic functions involving an operator having generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. In particular, Harnack’s Principle and Minimum Principle are provided for \(\mathcal {A}\)-superharmonic functions.
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Acknowledgements
I. Chlebicka is supported by NCN grant no. 2019/34/E/ST1/00120. A. Zatorska-Goldstein is supported by NCN grant no. 2019/33/B/ST1/00535.
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Chlebicka, I., Zatorska-Goldstein, A. Generalized Superharmonic Functions with Strongly Nonlinear Operator. Potential Anal 57, 379–400 (2022). https://doi.org/10.1007/s11118-021-09920-5
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DOI: https://doi.org/10.1007/s11118-021-09920-5
Keywords
- Superharmonic functions
- Harnack’s principle
- Poisson modification
- Minimum principle
- Liouville’s theorem
- Potential theory