AN INVERSE PROBLEM FOR THE p-LAPLACIAN: BOUNDARY DETERMINATION

作者：Salo Mikko^*; Zhong Xiao

来源：SIAM Journal on Mathematical Analysis, 2012, 44(4): 2474-2495.

DOI：10.1137/110838224

• inverse problem
• boundary determination
• p-Laplace operator

We study an inverse problem for nonlinear elliptic equations modeled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear Dirichlet-to-Neumann map. The result is constructive and local, and gives a method for determining the coefficient at a boundary point from measurements in a small neighborhood. The proofs work with the nonlinear equation directly instead of being based on linearization. In the complex valued case we employ complex geometrical optics-type solutions based on p-harmonic exponentials, while for the real case we use p-harmonic functions first introduced by Wolff.

• 出版日期2012