Geodesic
Well-posedness of discontinuous boundary-value problems for nonlinear elliptic complex equations in multiply connected domains
Electronic journal of differential equations, Tome 2013 (2013)
In the first part of this article, we study a discontinuous Riemann-Hilbert problem for nonlinear uniformly elliptic complex equations of first order in multiply connected domains. First we show its well-posedness. Then we give the representation of solutions for a modified Riemann-Hilbert problem for the complex equations. Then we obtain a priori estimates of the solutions and verify the solvability of the modified problem by using the Leray-Schauder theorem. Then the solvability of the original discontinuous Riemann-Hilbert boundary-value problem is obtained. In the second part, we study a discontinuous Poincare boundary-value problem for nonlinear elliptic equations of second order in multiply connected domains. First we formulate the boundary-value problem and show its new well-posedness. Next we obtain the representation of solutions and obtain a priori estimates for the solutions of a modified Poincare problem. Then with estimates and the method of parameter extension, we obtain the solvability of the discontinuous Poincare problem.
Classification : 35J56, 35J25, 35J60, 35B45
Keywords: well-posedness, discontinuous boundary value problem, nonlinear elliptic complex equation, A priori estimate, existence of solutions 
@article{EJDE_2013__2013__a73,
     author = {Wen,  Guo-Chun},
     title = {Well-posedness of discontinuous boundary-value problems for nonlinear elliptic complex equations in multiply connected domains},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.30036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a73/}
}
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%J Electronic journal of differential equations
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%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a73/
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Wen,  Guo-Chun. Well-posedness of discontinuous boundary-value problems for nonlinear elliptic complex equations in multiply connected domains. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a73/