Variational problems with free boundaries for the fractional Laplacian 论文
2010Journal of the European Mathematical Society引用 299顶会
Advanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsNumerical methods in inverse problems
摘要
We discuss properties (optimal regularity, non-degeneracy, smoothness of the free boundary...) of a variational interface problem involving the fractional Laplacian; Due to the non-locality of the Dirichlet problem, the task is nontrivial. This difficulty is by-passed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a co-dimension 2 (degenerate) free boundary.