From weak to strong convergence of the gradients for Finsler [formula omitted]-Laplacian problems as [formula omitted

Abstract

In this paper we investigate limits as p→∞ of solutions up to Finsler p-Laplacian problems −divF∗(x,∇up)p−1∂ξF∗(x,∇up)=f with f>0, coupled with a Dirichlet boundary condition up=g on ∂Ω. We prove that the whole sequence of solutions {up} converges to the limit function u∞strongly in W1,m(Ω) for any 1≤m<∞, provided that F∗(x,.) has some strict convexity on its unit sphere. We also characterize an explicit expression of the limit function.