## A note on the Monge–Ampère type equations with general source terms

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Weifeng Qiu and Lan Tang
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## Abstract:

In this paper we consider numerical approximation to the generalised solutions to the Monge–Ampère type equations with general source terms. We first give some important propositions for the border of generalised solutions. Then, for both the classical and weak Dirichlet boundary conditions, we present well-posed numerical methods for the generalised solutions with general source terms. Finally, we prove that the numerical solutions converge to the generalised solution.## References

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## Additional Information

**Weifeng Qiu**- Affiliation: Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong, People’s Republic of China
- MR Author ID: 845089
- Email: weifeqiu@cityu.edu.hk
**Lan Tang**- Affiliation: School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People’s Republic of China
- Email: lantang@mail.ccnu.edu.cn
- Received by editor(s): April 11, 2019
- Received by editor(s) in revised form: November 12, 2019, and February 11, 2020
- Published electronically: June 19, 2020
- Additional Notes: The first author was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11302219).

The second author was partially supported by NNSFC grant of China (No. 11831009) and the Fundamental Research Funds for the Central Universities (No. CCNU19TS032).

The second author is the corresponding author. - © Copyright 2020 American Mathematical Society
- Journal: Math. Comp.
**89**(2020), 2675-2706 - MSC (2010): Primary 65N30, 65L12
- DOI: https://doi.org/10.1090/mcom/3554
- MathSciNet review: 4136543