Uniqueness results for equations of the p(x)-Laplacian type
S. N. Antont︠s︡ev, Michel Marie Chipot, Yonghong Xie · Zurich Open Repository and Archive (University of Zurich) · 2007
We study uniqueness of weak solutions of elliptic equations of the type - div (a(x,u,∇u))+b(x,u)=f(x) in a bounded domain Ω⊂ℝ n with Lipschitz boundary γ=∂Ω. We consider in particular mixed boundary conditions - i.e. Dirichlet condition on one part of the boundary and Neumann condition on the other part. A model equation could be - div (a(x,u)|∇u|p(x)-2∇u)+b(x,u)=f(x),x∈Ω· We establish uniqueness results for these equations. We also indicate conditions which guarantee existence of solution.