On general boundary-value problems for nonlinear elliptic equations of second order in a multiply connected plane domain

✍ Scribed by Guo-Chun Wen; Chung-Chun Yang

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 762 KB
• Volume: 43
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00047923

✦ Synopsis

This paper deals with some general irregular oblique derivative problems for nonlinear unilbrmly elliptic equations of second order in a multiply connected plane domain. Firstly, we state the well-posedness of a new set of modified boundary conditions. Secondly, we verify the existence of solutions of the modified boundary-value problem for harmonic functions, and then prove the solvability of the modified problem for nonlinear elliptic equations, which includes the original boundary-value problem (i.e. boundary conditions without involving undertermined functions data). Here, mainly, the location of the zeros of analytic functions, a priori estimates for solutions and the continuity method are used in deriving all these results. Furthermore, the present approach and setting seems to be new and different from what has been employed before.