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Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: A probabilistic approach

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Abstract

In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equations and quasi-derivatives.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11631004) and Science and Technology Commission of Shanghai Municipality (Grant No. 14XD1400400). The authors are grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Jun Dai, Shanjian Tang & Bingjie Wu

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  1. Jun Dai
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  2. Shanjian Tang
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  3. Bingjie Wu
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Correspondence to Shanjian Tang.

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Dai, J., Tang, S. & Wu, B. Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: A probabilistic approach. Sci. China Math. 62, 1851–1886 (2019). https://doi.org/10.1007/s11425-018-9375-5

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  • DOI: https://doi.org/10.1007/s11425-018-9375-5

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