A Neumann problem for the p(x)-Laplacian with p=1 in a sub domain

作者：Karagiorgos Yiannis; Yannakakis Nikos^*

来源：Journal of Mathematical Analysis and Applications, 2017, 454(1): 412-428.

DOI：10.1016/j.jmaa.2017.05.004

• Neumann problem
• p(x)-Laplacian
• 1-Laplacian
• BV space

In this paper we study a Neumann problem with non-homogeneous boundary conditions for the p(x)-Laplacian. In particular we assume that p(.) is a step function defined in a domain Omega and equals to 1 in a subdomain Omega(1) and 2 in its complementary Omega(2). By considering a suitable sequence p(k) of variable exponents such that pk -> p and replacing p with p(k) in the original problem, we prove the existence of a solution u(k) for each of those intermediate ones. We also show, that under a hypothesis concerning the boundary data g, the limit of the sequence (u(k)) is a function u, which belongs to the space of functions of bounded variation and is a solution to the original p(.)-problem.

• 出版日期2017-10-1