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On the Existence of \(L^p\)-Solution of Generalized Euler–Poisson–Darboux Equation in the Upper Half Space

  • Kangqun ZhangEmail author
Article

Abstract

We focus on the existence of solution of generalized Euler–Poisson–Darboux equation, which is elliptic in \(\mathbb R^{n+1}_+\) and has a singular coefficient on its boundary. Based on Mikhlin’s multiplier theorem and Hardy inequalities, the well-posedness of its Dirichlet problem in the upper half space is established.

Keywords

Generalized Euler–Poisson–Darboux equation Elliptic type \(L^p\)-solution 

Mathematics Subject Classification

35Q05 35J75 

Notes

Acknowledgements

We sincerely thank the anonymous referees for their comments and useful suggestions. This work was partially supported by NNSF of China (11326152), NSF of Jiangsu Province of China (BK20130736), NSF of the Jiangsu Higher Education Institutions of China (18KJB110013) and NSF of Nanjing Institute of Technology (CKJB201709).

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Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsNanjing Institute of TechnologyNanjingChina

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