3:00 pm Friday, October 4, 2019
Junior Analysis: The Pohozaev Identity: Classical and Fractional Versions by María Soria-Carro in RLM 11.176
In 1965, S. Pohozaev proved the nonexistence of positive solutions to some semilinear problems with supercritical nonlinearities in star-shaped domains. His proof is based on an identity, which is nowadays known as Pohozaev identity. In this talk, we will prove this result, which follows from the divergence theorem and integration by parts formula. More recently, in 2014, X. Ros-Oton and J. Serra showed a Pohozaev identity for the fractional Laplacian. In the nonlocal framework, the classical tools are not available, and thus, they need to follow a different approach. One of the main difficulties is to establish the boundary regularity of solutions to the Dirichlet problem. The proof is technical so we will only focus on the main ideas. Submitted by
|
|