The solution of Riemann-Hilbert boundary value problem for elliptic complex equations of first order in the Sobolev space \(W_ p^ l(D)\) \((1<p<2)\). (English) Zbl 0742.35023
We give a new proper formulation of the Riemann Hilbert boundary value problem for nonlinear elliptic complex equations of first order in a general multiply connected domain and establish related existence and uniqueness theorems for solutions in the Sobolev space \(W^ 1_ p(D) (1<p<2)\).
Reviewer: P.Li (Yantai)
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 35A07 | Local existence and uniqueness theorems (PDE) (MSC2000) |
