Abstract
We prove a uniqueness theorem for the obstacle problem for linear equations involving the fractional Laplacian with zero Dirichlet exterior condition. The problem under consideration arises as the limit of some logistic-type equations. Our result extends (and slightly strengthens) the known corresponding results for the classical Laplace operator with zero boundary condition. Our proof, as compared with the known proof for the classical Laplace operator, is entirely new, and is based on the probabilistic potential theory. Its advantage is that it may be applied to a wide class of integro-differential operators.
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Acknowledgements
This work was supported by Polish National Science Centre(Grant No. 2017/25/B/ST1/00878). Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
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Klimsiak, T. Uniqueness for an Obstacle Problem Arising from Logistic-Type Equations with Fractional Laplacian. Potential Anal 59, 897–916 (2023). https://doi.org/10.1007/s11118-022-09986-9
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DOI: https://doi.org/10.1007/s11118-022-09986-9