Existence results for some nonlinear elliptic equations with measure data in Orlicz-Sobolev spaces

Ge Dong  (Ph.D, Tongji University)

15:00 pm to 16:00 pm, May 12th, 2015   Science Building A1510

Abstract:

We prove the existence results in the setting of Orlicz spaces for the following nonlinear elliptic equation $A(u) + g(x, u, Du) = \mu$ , where A is a Leray-Lions operator defined on $D(A) \subset W_0^1 L_M(\Omega)$, while $g$ is a nonlinear term having a growth condition with respect to $Du$, but does not satisfy any sign condition. The right-hand side $\mu$ is a bounded Radon measure data.