An optimal transportation problem related to the limits of solutions of local and nonlocal -Laplace-type problems

作者：Jylha Heikki^*

来源：Revista Matematica Complutense, 2015, 28(1): 85-121.

DOI：10.1007/s13163-014-0147-5

• Optimal transportation
• Nonlocal equation
• p-Laplace equation

We investigate the asymptotic behavior of minimizers of problems related to the -Laplace equation . As , the minimizers converge (up to a subsequence) to a function, which maximizes the functional with appropriate constraints. The main result of this paper is that the problem of maximizing with Dirichlet boundary condition can be identified as a dual problem of a certain mass transportation problem. Our approach applies to the limits of both -Laplace type problems in classical Sobolev spaces and analogous nonlocal problems in fractional Sobolev spaces.

• 出版日期2015-1