|DATE||March 02 (Fri), 2018|
|TITLE||Gradient estimates for double phase problems|
In this talk, we consider a non-linear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We first introduce a Calderon-Zygmund theory for a double phase problem with (p,q)-growth. And then we establish a gradient estimate for a double phase problem with an irregular obstacle by proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence.