IJPAM: Volume 91, No. 3 (2014)

THE NEW WELL-POSEDNESS OF DISCONTINUOUS
RIEMANN-HILBERT PROBLEM FOR ELLIPTIC COMPLEX
EQUATIONS OF FIRST ORDER WITH
TWO DEGENERATE LINES

G.C. Wen$^1$, Y.H. Zhang$^2$
$^1$LMAM, School of Mathematical Sciences
Peking University
Beijing, 100871, P.R. CHINA
$^2$Department of Mathematics
Beijing Technology and Business University
Beijing, 100048, P.R. CHINA


Abstract. This article deals with some elliptic complex equations of first order, i.e. the generalized Beltrimi equation with two degenerate lines in the discussed multiply connected domain. We first propose the new well-posed-ness of discontinuous Riemman-Hilbert problem, give estimates of solutions for the modified boundary value problem. Afterwards by using the method of parameter extension, the existence of continuous solutions for the generalized Beltrimi equation is verified. In the article, the proof of H$\ddot{\rm o}$lder continuity of a singular double integer is very difficult and interesting. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order.

Received: December 3, 3013

AMS Subject Classification: 35J60, 35J70, 35J56

Key Words and Phrases: elliptic complex equations, two degenerate lines, the new posed-ness of discontinuous Riemann-Hilbert problem, unique solvability of continuous solutions, H$\ddot{\rm o}$lder continuity of singular integer

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DOI: 10.12732/ijpam.v91i3.15 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 3