Abstract
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (ellipti-chyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of Hölder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.
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Supported in part by the National Natural Science Foundation of China under Grant No. 11021161 and 10928102, 973 Program of China under Grant No. 2011CB80800, Chinese Academy of Sciences under Grant No. kjcx-yw-s7, project grant of “Center for Research and Applications in Plasma Physics and Pulsed Power Technology, PBCT-Chile-ACT 26” and Dirección de Programas de Investigación, Universidad de Talca, Chile.
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Wen, Gc. The Riemann-Hilbert problem for mixed complex equations of first order with degenerate rank 0. Acta Math. Appl. Sin. Engl. Ser. 31, 31–42 (2015). https://doi.org/10.1007/s10255-014-0408-6
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DOI: https://doi.org/10.1007/s10255-014-0408-6
Keywords
- Riemann-Hilbert problem
- quasilinear mixed complex equations
- degenerate rank 0
- unique solvability of the problem
- Hölder continuity of singular double integer