Abstract
In this paper, we establish existence and uniqueness of weak (Sobolev) solution to the third boundary value problem for a class of semilinear elliptic partial differential equations with singular coefficients. Our method is probabilistic. The gauge theory and backward stochastic differential equations with singular coefficients play an important role in our approach.
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Acknowledgements
The authors would like to thank the anonymous referee for careful reading and valuable comments that led to the improvement of this work.
This work was partially supported by NSF of China (No.11871476).
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Duan, J., Peng, J. The Probabilistic Solution of a System of Semilinear Elliptic PDEs Under the Third Boundary Conditions. Potential Anal 59, 1571–1597 (2023). https://doi.org/10.1007/s11118-022-10025-w
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DOI: https://doi.org/10.1007/s11118-022-10025-w