Pohozaev identities for anisotropic integrodifferential operators

摘要

We find and prove new Pohozaev identities and integration by parts type formulas for anisotropic integrodifferential operators of order 2s, with s is an element of (0,1). These identities involve local boundary terms, in which the quantity u/d(s)backslash(partial derivative Omega) plays the role that partial derivative u/partial derivative v plays in the second-order case. Here, u is any solution to Lu = f(x,u) in ,Omega, with u = 0 in R-n backslash Omega, and d is the distance to partial derivative Omega.