On Boundary Value Problems for Degenerate Quasilinear Elliptic Equations and Inequalities

✍ Scribed by Vy Khoi Le; Klaus Schmitt

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 500 KB
• Volume: 144
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1997.3384

✦ Synopsis

We are concerned with quasilinear partial differential equations of elliptic type which are degenerate; in particular we investigate the range of such quasilinear differential operators and properties of the solution operator. For elliptic problems which are semilinear in nature, much has been accomplished in recent years, whereas for more general quasilinear or fully nonlinear problems such information is by comparison very incomplete.

Let us briefly describe the problem to be studied here.

Let 0 be a bounded open set in R N and let

be a mapping satisfying Carathe odory conditions which has the asymptotic behavior

where w is a nonnegative measurable function satisfying certain additional conditions,

where : and ; are positive constants and p # (1, ). Also A is assumed to be strictly monotone with respect to v i.e.

We consider boundary value problems of the following type &div A(x, {u)=f, x # 0, (2) u=%,

x # 0.