Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type |
| |
Authors: | Mokhtar Kirane Nasser-Eddine Tatar |
| |
Institution: | (1) Université de La Rochelle, La Rochelle, France;(2) King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia |
| |
Abstract: | We consider the Laplace equation in ? d?1 × ?+ × (0,+∞) with a dynamical nonlinear boundary condition of order between 1 and 2. Namely, the boundary condition is a fractional differential inequality involving derivatives of noninteger order as well as a nonlinear source. Nonexistence results and necessary conditions are established for local and global existence. In particular, we show that the critical exponent depends only on the fractional derivative of the least order. |
| |
Keywords: | critical exponent dynamical boundary condition fractional derivative Laplace equation |
本文献已被 SpringerLink 等数据库收录! |