JournalszaaVol. 27 , No. 3DOI 10.4171/zaa/1356

Discontinuous Irregular Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order

  • Guochun Wen

    Peking University, Beijing, China
  • Zuoliang Xu

    Renmin University of China, Beijing, China
Discontinuous Irregular Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order cover

Abstract

In this paper, the discontinuous irregular oblique derivative problems (or discontinuous Poincareˊ{\rm\acute e} boundary value problems) for nonlinear elliptic equations of second order in multiply connected domains are discussed by using a complex analytic method. Firstly the uniqueness of solutions for such boundary value problems is proved and a priori estimates of their solutions are given, and then by the Leray-Schauder theorem, the existence of solutions of the above problems is verified. As a special case the result about the continuous irregular oblique derivative problem for the nonlinear equations is derived.