Uniqueness of Nonnegative Solutions to Elliptic Differential Inequalities on Finsler Manifolds

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We consider a class of elliptic differential inequalities involving Finsler p-Laplacian and a positive potential function on forward geodesically complete noncompact Finsler measure spaces with finite reversibility. Under various volume growth conditions concerning geodesic balls with a given center and the potential function, we prove that the only nonnegative weak solution of the differential inequalities is identically zero.

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Correspondence to Changwei Xiong.

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This research was supported by Australian Laureate Fellowship FL150100126 of the Australian Research Council. We would like to thank the referee for careful reading of the paper and for valuable suggestions and comments which made this paper better and more readable. We are also grateful to Ben Andrews for his support.

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Xiong, C. Uniqueness of Nonnegative Solutions to Elliptic Differential Inequalities on Finsler Manifolds. Potential Anal 53, 1145–1163 (2020). https://doi.org/10.1007/s11118-019-09801-y

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  • Uniqueness of nonnegative solutions
  • Elliptic differential inequality
  • Finsler measure space

Mathematics Subject Classification (2010)

  • 35R45
  • 35J92
  • 58J05