Abstract
In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann-Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.
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Wen, G.C. The discontinuous Riemann-Hilbert problem for elliptic complex equations of first order. Acta. Math. Sin.-English Ser. 29, 2233–2244 (2013). https://doi.org/10.1007/s10114-013-2805-9
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DOI: https://doi.org/10.1007/s10114-013-2805-9
Keywords
- Discontinuous Riemann-Hilbert problems
- elliptic complex equations
- estimates and existence of solutions
- multiply connected domains