Abstract
We consider, for a bounded open domain Ω in Rn and a function u : Ω → Rm, the quasilinear elliptic system: (1). We generalize the system (QES)(f,g) in considering a right hand side depending on the jacobian matrix Du. Here, the star in (QES)(f,g) indicates that f may depend on Du. In the right hand side, v belongs to the dual space W-1,P’(Ω, ω*, Rm), , f and g satisfy some standard continuity and growth conditions. We prove existence of a regularity, growth and coercivity conditions for σ, but with only very mild monotonicity assumptions.
Highlights
In this paper, the main point is that we do not require monotonicity in the strict monotonicity of a typical Leray-Lions operator as it is usually assumed in previous papers
The Ball theorem [1] and especially the resulting tool mode available by Hungerbühler to partial differential equation theory give them a sufficient control on the gradient approximating sequence Duk to pass to the limit
Visik [9] and mainly by Hungurbühler to get the existence of a weak solution for the quasi-linear elliptic system [10]
Summary
The main point is that we do not require monotonicity in the strict monotonicity of a typical Leray-Lions operator as it is usually assumed in previous papers The aims of this text are to prove analogous existence results under relaxed monotonicity, in particular under strict quasi-monotonicity. The Ball theorem [1] and especially the resulting tool mode available by Hungerbühler to partial differential equation theory give them a sufficient control on the gradient approximating sequence Duk to pass to the limit. This method is used by Dolzmann [2], G. This kind of problems finds its applications in the model of Thomas-Fermis in atomic physics [12], and porous flow modeling in reservoir [13]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
