The Cauchy problem for nonlinear elliptic equations

✍ Scribed by Ibrahim Ly; Nikolai Tarkhanov

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 693 KB
• Volume: 70
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.03.034

✦ Synopsis

This paper is devoted to investigation of the Cauchy problem for nonlinear equations with a small parameter. They are actually small perturbations of linear elliptic equations in which case the Cauchy problem is ill-posed. To study the Cauchy problem we invoke purely nonlinear methods, such as successive iterations and L q Sobolev spaces with large q. We also discuss linearisable problems.